RPSEA
FINAL TECHNICAL REPORT
Document Number: 08121-2902-07.FINAL
Fiber-containing Sweep Fluids for Ultra Deepwater Drilling Applications
Contract Number: 08121-2902-07
March 3, 2012
Ramadan M. Ahmed
Assistant Professor
The University of Oklahoma
100 Boyd St., Norman, OK 73019
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LEGAL NOTICE
This report was prepared by The University of Oklahoma as an account of work sponsored by
the Research Partnership to Secure Energy for America, RPSEA. Neither RPSEA members of
RPSEA, the National Energy Technology Laboratory, the U.S. Department of Energy, nor any
person acting on behalf of any of the entities:
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REPORTED HEREIN SHOULD BE TREATED AS PRELIMINARY.
REFERENCE TO TRADE NAMES OR SPECIFIC COMMERCIAL PRODUCTS, COMMODITIES, OR
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COMMERCIAL PRODUCT, COMMODITY, OR SERVICE.
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Abstract
This report presents experimental and theoretical studies conducted on the rheology and stability of fiber-
containing sweep fluids. In addition, the report shows results of our investigations on settling behavior of
solids particles in fiber sweeps. Spherical glass particles with different diameters were used. We
performed experiments using water and oil-based fluids. Fluid composition and fiber concentration were
varied during the investigation.
Rheological properties of the fluid samples were measured before stability and settling velocity
experiments. Even though 0.04 percent fiber content is recommended in the field for sweep application,
tests were conducted varying fiber content from 0.00 to 0.08 percent. Results indicate the absence of
excessive thickening, which is frequently observed in highly concentrated fiber suspensions. Because of
their low fiber concentration, fiber sweeps are not vulnerable to excessive thickening.
The stability of fiber sweep determined the hole-cleaning performance of the fluid. During our
investigations, we developed mathematical models based on hydrodynamic drag behavior of long
cylinders. They predict the stability of non-Newtonian fiber suspensions. Model predictions showed good
agreement with experimental results. Both theoretical analysis and experimental observation suggested
the critical role of viscosity in maintaining the stability of the fluid. Highly viscous base fluids created
stable fiber suspensions. However, viscosity was not the only parameter that controlled the stability of
these fluids. The polymer type also played a great role. In general, xanthan gum-based fluids showed
very good stability. In addition to the polymer type, the existence of structure in the fluid also stabilized
the fluid. Oil-based muds (OBM and SBM) are structured fluids with a continuous oil phase and
dispersed water droplets. Because of the surfactant (i.e., emulsifier), the fluid maintained its structure for
sufficiently long time. The structure trapped fiber particles and kept them in the suspension without
segregation. All oil-based fluids that were tested show excellent stability.
Settling velocity of cuttings is often used to assess hole-cleaning performance of drilling fluids. The
addition of fiber into a drilling fluid substantially reduced the settling velocity of cuttings and improved
carrying capacity of the fluid. The velocity reduction came from the improvement of the drag force that
opposes the motion of the particle. When fiber particles were fully dispersed in the fluid, they tended to
form a network structure that generated additional drag force (fiber drag). After obtaining settling velocity
measurements, we were able to determine the contribution of the fiber drag to the total drag force. Due to
the strong interactions between the fiber particles and the base fluid, the hydrodynamic component of the
fiber drag dominated the drag that originated because of mechanical friction and fiber entanglement. As a
result, the fiber drag was strongly related to viscous properties of the fluid. In this study, we developed a
settling velocity model by predicting settling behavior of particles in fiber sweeps. The model accounted
for the presence of fiber particle using the fiber drag coefficient. Model predictions showed a satisfactory
agreement with experimental measurements.
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Sweep experiments were conducted with fiber-containing water-based and synthetic-based drilling fluids
to study wellbore cleaning performance. Extensive flow loop experiments were carried out by varying
fiber concentration (up to 0.27 lb/bbl) in industry utilized water-based and synthetic-based drilling fluid
formulations. Cuttings bed heights in the flow loop annulus were measured at different flow rates and
pipe rotation speeds for the different fluid-fiber combinations at horizontal and inclined configurations. In
addition, to investigate the hydraulic impact of the fiber, pipe viscometer and wellbore hydraulics
experiments were conducted at varying fiber concentrations. Results showed that fiber sweeps
substantially improved cuttings removal compared to the base fluid sweeps, despite similar equivalent
circulating densities.
A mechanistic model was developed to predict critical cuttings transport velocity or equilibrium bed
height in horizontal and inclined wellbores with fiber-containing fluids. The model was developed by
considering fluid flow over a stationary bed of solid particles of uniform thickness. The model required a
correlation for estimating the additional drag (i.e., fiber drag) resulting from the presence of fiber in the
fluid. Settling velocity experimental data was used to provide a correlation for the fiber drag coefficient,
and the sweep experiments were used to verify the model predictions. The critical transport velocity was
measured by visual observation of the cuttings bed particles movement. The model predictions and
experimental measurements showed good agreement at low flow rates. For fluids without fiber (i.e., base
fluid), mechanistic model predictions were compared with published experimental results and with
predictions of an existing model. The comparisons showed satisfactory agreement with measurements and
better accuracy than the existing model.
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Table of Contents
Disclaimer
Abstract
Table of Contents
List of Tables
List of Figures
1. Executive Summary
2. Theoretical Study on Stability of Fiber Sweeps
2.1. Particle Settling Behavior
2.1.1. Classification of Particle Settling Behavior
2.1.2. Motion of Fibrous Particles
2.2. Modeling Rising Velocity of Particles
2.3. Non-Rising Particles under Static Conditions
2.4. Non-Rising Particles under Dynamic Conditions
2.5. Modeling Results
2.6. Conclusions
Nomenclature
References
3. Experimental Study on Stability of Fiber Sweeps
3.1. Scope
3.2. Experimental Setup and Procedure
3.3. Results
3.3.1. Effect of Base Fluid Rheology on Stability of Fiber Sweep
3.3.2. Effect of Temperature on Stability of Fiber Sweep
3.3.3. Comparison of Model Predictions with Experimental Results
3.4. Conclusions
Nomenclature
References
4. Rheological Properties of Fiber Sweeps
4.1. Introduction
4.2. Literature Review
4.3. Fiber Fluid Rheology
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4.4. Experimental Investigations
4.4.1. Experimental Setup
4.4.2. Test Procedure
4.5. Experimental Results
4.5.1. Effect of Fiber Concentration
4.5.2. Effect of Temperature
4.5.3. Shear Viscosity Parameters
4.6. Conclusions
Nomenclature
References
5. Settling Behavior of Particles in Fiber-containing Drilling Fluids
5.1. Introduction
5.2. Settling in Fiber Suspensions
5.3. Experimental Study
5.3.1. Experimental Setup
5.3.2. Test Materials
5.3.3. Test Procedure
5.3.4. Test Results
5.4. Analysis of Results and Discussions
5.5. Model Predictions
5.6. Conclusions
Nomenclature
References
6. Hole Cleaning Performance of Fiber Sweeps
6.1. Introduction
6.2. Experimental Setup
6.3. Experimental Procedure
6.4. Experimental Test Matrix
6.4.1. WBM Test Matrix
6.4.2. SBM Test Matrix
6.5. Experimental Results
6.5.1. Dynamic Variation of Cuttings Bed Height
6.5.2. Effect of Fluid Types
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6.5.3. Effect of Fiber Concentration
6.5.4. Effect of Inclination Angle
6.5.5. Effect of Flow Rate
6.5.6. Effect of Pipe Rotation
6.6. Pipe Viscometer Measurements
6.7. Wellbore Hydraulics
6.8. Conclusions
6.9. Guidelines
Nomenclature
References
7. Mechanistic Modeling of Hole Cleaning with Fiber Sweeps
7.1. Introduction
7.2. Forces Involved in Particle Transport
7.2.1. Gravity and Buoyancy Forces
7.2.2. Hydrodynamic Forces
7.2.3. Fiber Drag Force
7.2.4. Plastic Force
7.3. Near-Bed Velocity Profile
7.3.1. Newtonian Fluid
7.3.2. Non-Newtonian Fluid
7.4. Mechanistic Model Formulation
7.5. Experimental Results
7.5.1. Comparison of Model Predictions with Test Measurements
7.5.2. Comparison of Model Predictions with Published Data and Existing Model
7.6. Conclusions
Nomenclature
References
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List of Tables
Table 2.1
Table 3.1
Table 3.2
Table 4.1
Table 4.2
Table 4.3
Table 4.4
Table 4.5
Table 4.6
Table 4.7
Table 4.8
Table 6.1
Table 6.2
Input data
Test matrix for stability experiments
One-hour stability of test fluids
Test matrix of rotational viscometer measurements
Fiber properties
Rheological parameters of XG based fluid with varying fiber concentration at 72°F and 170°F
Rheological parameters of PAC based fluid with varying fiber concentration at 72°F and 170°F
Rheological parameters of XG/PAC (50%/50%) based fluid at 72°F and 170°F
Rheological parameters of XG + Barite (12 ppg) based fluid at 72°F and 170°F
Rheological parameters of PHPA based fluid with varying fiber concentration at 72°F and 170°F
Rheological parameters of OBM and SBM with varying fiber concentration at 72°F and 170°F
WBM flow loop test matrix and rheological properties
SBM flow loop test matrix
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List of Figures
Fig. 2.1
Fig. 2.2
Fig. 2.3
Fig. 2.4
Fig. 2.5
Fig. 2.6
Fig. 2.7a
Fig. 2.7b
Fig. 2.8
Fig. 2.9
Fig. 2.10
Fig. 2.11
Fig. 2.12
Fig. 3.1
Fig. 3.2
Fig. 3.3
Fig. 3.4
Fig. 3.5
Fig. 3.6
Fig. 3.7
Fig. 3.8
Fig. 3.9
Fig. 3.10
Fig. 3.11
Fig. 3.12
Fig. 3.13
Fig. 3.14
Free body diagram of a cylindrical particle rising in static fluid
Vertical component of shear force acting on a fully suspended cylinder
Differential element of a cylinder subject to shear force
Shear force acting on a cylinder oriented vertically
Critical yield stress as a function of fluid density for a non-raising particle
Narrow slot representing annulus
Rising velocity vs. yield stress for horizontally oriented fiber in 8.33 ppg fluid with n=0.3
Rising velocity vs. yield stress for horizontally oriented fiber in 8.33 ppg fluid with n=0.6
Rising velocity vs. yield stress for horizontally oriented fiber in 8.33 ppg fluid with n=1.0
Rising velocity vs. yield stress for horizontally oriented fiber (n = 0.3 & K = 2.1 lbfsn/100 ft
2)
Rising velocity vs. yield stress for horizontally oriented fiber (n = 0.6 & K = 2.1 lbfsn/100 ft
2)
Rising velocity vs. yield stress for horizontally oriented fiber (n = 1.0 & K = 2.1 lbfsn/100 ft
2)
Rising velocity vs. mud weight under dynamic conditions for vertically oriented fiber
Fluid samples
Unstable fluids after 1-hour test
Graduated cylinder used for stability experiment
One-hour stabilities of XG based fiber sweep at 170°F
One-hour stabilities of PAC based fiber sweeps at 170°F
One-hour stabilities of PHPA based fiber sweeps at 170°F
One-hour stabilities of XG/PAC based fiber sweeps at 170°F
One-hour stabilities of XG based weighted (12 ppg) fiber sweeps at 170°F
Measured and predicted one-hour stability of oil-based fluids at 170°F
Twelve-hour stabilities of XG based fluids at 170°F
Twelve-hour stabilities of XG based fluids at 72°F
One-hour stabilities of PAC based fluids at 72°F
Half-hour stabilities of PAC based fluids at 170°F
Apparent viscosity vs. shear rate of based fluids at 170°F
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Fig. 4.1
Fig. 4.2
Fig. 4.3
Fig. 4.4
Fig. 4.5
Fig. 4.6
Fig. 4.7
Fig. 4.8
Fig. 5.1
Fig. 5.2
Fig. 5.3
Fig. 5.4
Fig. 5.5
Fig. 5.6
Fig. 5.7
Fig. 5.8
Fig. 5.9
Fig. 5.10
Fig. 5.11
Fig. 5.12
Fig. 6.1
Fig. 6.2
Fig. 6.3
Fig. 6.4
Fig. 6.5
Fig. 6.6
Fig. 6.7
Fig. 6.8
Stand mixers
Rotational viscometers
Rheology of XG based fluid at 72°F and 170°F varying fiber and polymer concentrations
Rheology of PAC based fluid at 72°F and 170°F varying fiber and polymer concentrations
Rheology of XG/PAC (50%/50%) mix fluid at 72°F and 170°F
Rheology of XG based weighted fluids (12 ppg) at 72°F and 170°F
Rheology of PHPA based fluids at 72°F and 170°F varying fiber and polymer concentrations
Rheology of weighted (12.2 ppg) oil-based fluids at 72°F and 170°F
Schematic of the settling cylinder
Rheologies of 0.5% PAC based fluids with different fiber concentrations
Settling velocity of 2-mm glass bead vs. time in mineral oil
Drag coefficient vs. particle Reynolds Number for base fluids
Settling velocity particle in 0.5% PAC based fluid for different fiber concentrations
Settling velocity particle in 0.25% XG based fluid for different fiber concentrations
Comparison of fiber drag with viscous drag acting on a particle in 0.5% PAC based fluid
Fiber drag coefficient vs. Reynolds Number
Normalized fiber drag coefficient vs. Reynolds Number for different fluids
Predicted vs. measured settling velocity for different PAC based fluids
Predicted and measured settling velocity vs. fiber concentration for 0.5% PAC
Predicted and measured settling velocity vs. fiber concentration for 0.25% XG
Flow loop in inclined position
Flow loop configuration/schematic
Sieve analysis of silica sand, 8/16 mesh
Synthetic-based fluid constituents
Packaged components of synthetic-based fluid
SBM component concentrations
Emulsifier/Dispersator
Annulus test section bed height measuring tapes
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Fig. 6.9
Fig. 6.10
Fig. 6.11
Fig. 6.12
Fig. 6.13
Fig. 6.14
Fig. 6.15
Fig. 6.16
Fig. 6.17
Fig. 6.18
Fig. 6.19
Fig. 6.20
Fig. 6.21
Fig. 6.22
Fig. 6.23
Fig. 6.24
Fig. 6.25
Fig. 6.26
Fig. 6.27
Fig. 6.28
Fig. 6.29
Fig. 6.30
Fig. 6.31
Fig. 7.1
Fig. 7.2
Fig. 7.3
Fig. 7.4
Fig. 7.5
Bed height vs. flow rate for XG based fluid sweep (no fiber), inclined annulus (8.33 ppg)
Fluctuation of cuttings bed height due to drillpipe rotation
Bed height vs. flow rate for WBM and SBM, no rotation, inclined annulus
Percent reduction of bed height of WBM and SBM, no rotation, inclined annulus
Apparent viscosity vs. shear rate for sweep base fluids, ~95°F
Bed height vs. flow rate for WBM, no rotation, inclined annulus
Comparison of fiber effectiveness for hole cleaning with WBM (8.33 ppg), inclined annulus
Dimensionless bed height vs. flow rate for SBM, no pipe rotation
Dimensionless bed height vs. flow rate for WBM, no pipe rotation, horizontal annulus
Percent bed height reduction vs. fiber concentration for SBM, no pipe rotation
Percent bed height reduction vs. flow rate for SBM, no pipe rotation
Percent bed height reduction vs. flow rate for SBM, 25 rpm pipe rotation
Percent bed height reduction vs. inclination angle for SBM
Dimensionless bed height vs. flow rate for WBM base fluid, horizontal and inclined annulus
Percent bed height reduction vs. flow rate for SBM base sweep, no fiber
Effect of different pipe rotation speeds on the hole cleaning for WBM
Percent bed height reduction vs. fiber concentration for SBM, Q = 20 gpm
Pipe viscometer schematic
Measured pressure loss as a function of flow rate in pipe viscometer, 90° orientation
Friction factor vs. General Reynolds number in pipe viscometer, 90° orientation
Annulus test section schematic
Measured pressure loss as a function of flow rate in annulus, 90° orientation
WBM Friction factor vs. General Reynolds number in annulus, 90° orientation
Forces acting on a single bed particle
Drag and lift force acting on the surface of a bed particle
Stagnant fluid surrounding a bed particle (Ahmed et al. 2002)
Bed height vs. flow rate for 2 mm cuttings in horizontal configuration
Bed height vs. flow rate for 2 mm cuttings in inclined (70°) configuration
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Fig. 7.6
Fig. 7.7
Bed height vs. flow rate for 0.45 mm cuttings with PAC based fluid
Bed height vs. flow rate for 0.45 mm cuttings with PAC based fluid
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1 | P a g e
1. Executive Summary
Project Management Plan and Technology Status Assessment (Tasks 1 & 2): The project began with
developing the project management plan and assessing the technology status. As required by RPSEA, the
project management plan and technology status assessment report were submitted within 30 days of the
award. The project management plan presents project work breakdown structure, schedules, key
milestones, and planned expenditures for each Task.
Technology Transfer, Project Reporting and Other Activities (Tasks 3 & 4): Different technology
transfer methodologies are being implemented to disseminate the outcomes of the project. Project
outcomes have been presented in different meetings including: Six RPSEA TAC meetings and MPGE
advisory board meeting. A paper on rheology of fiber sweeps (George et al. 2011) was presented at the
2011 AADE meeting. We participated in the 2011 Offshore Technology Conference (OTC), University
showcase. Furthermore, a book chapter (George et al. 2012) and a journal article (Elgaddafi et al. 2012)
have been accepted for publication.
Literature Review and Theoretical Study (Task 5): The research part of the project began with
extensive literature review on fiber-containing fluid systems. Literature review and theoretical
investigations on rheology, hydraulics, stability and carrying capacity of fiber-containing drilling sweeps
were undertaken. The outcomes of this task that are presented in Sections 2, 4, and 5 were used to develop
a mechanistic model to predict the hole cleaning performance of fiber sweeps. The model optimizes fiber
sweep applications.
Bench-Top Experiments (Task 6): These experiments were aimed at developing fiber sweep
formulations that have superior stability and optimum fiber concentration. We developed a stability model
for fiber sweeps and theoretically analyzed their stability (Section 2). This helped us to select the ranges
of base fluid properties that are suitable for fiber sweep applications. The stability of commonly used base
fluids were tested and stable formulations identified (Section 3). Even though excessive thickening is a
common problem with fibrous fluids, our rheology study (Section 4) did not demonstrate the presence of
thickening in fiber sweeps. As the fiber concentration increased, the rheologies of test samples remained
roughly the same. In addition to stability and rheology studies, extensive settling experiments were
carried out (Section 5) to assess carry capacity of fiber sweeps. Based on theoretical analysis and
experimental results, we developed a model that predicts the settling behavior of particles in fiber sweeps.
The model was applied to formulate the mechanistic hole-cleaning model, which was developed in Task
8.
2 | P a g e
Flow Loop Experiments (Task 7): Extensive flow loop experiments were carried out to study rheology,
hydraulics and hole cleaning performance of the base fluids and fiber sweeps. To conduct the
experiments, first the flow loop was modified to perform fiber sweep tests. Fiber concentration,
inclination angle, and pipe rotational speed were varied. Water-based and synthetic-based fluids were
tested. Results showed the hole cleaning performance of the fiber sweep under different conditions.
Mechanistic Modeling (Task 8): Flow loop measurements may not be directly applied to evaluate the
performance of sweep fluid in the field. However, they can be used to validate and calibrate models that
are based on the generalized conservation laws and applicable for both field and lab-scale measurements.
Therefore, in the final stage of the project, modeling study was carried out to formulate a mechanistic that
predicted the performance of the sweep fluid under field conditions and optimized the application of fiber
sweep technology. Flow loop measurements were utilized to evaluate and calibrate the model.
Deliverables of the project:
i. Report and publications presenting:
• Literature review findings (Sections 2.1, 4.2 and 5.1) and data analysis (Sections 3.3, 4.5, 5.4
and 6.4)
• Empirical correlations and semi-empirical models (Section 5.4)
• Mathematical models (Sections 7, 5.2 and 2.2), and
• Mechanisms and physical phenomena involved in the application of fiber sweep (Sections
2.1, 3, 4.1 and 5.1)
ii. Formulations of stable fiber-containing sweep fluids (Section 3.3)
iii. Experimental data describing
• Particle settling velocity (Section 5.3)
• Fiber drag (Section 5.4)
• Rheology and stability under different temperature conditions (Sections 3 and 4)
• Hydraulics and hole cleaning performance of fiber sweeps (Section 6)
iv. Recommendations and guidelines for field applications (Section 6.9)
References
George, M., Ahmed, R. and Growcock, F. 2011.Rheological Properties of Fiber-Containing Drilling
Sweeps at Ambient and Elevated Temperatures, paper AADE-11-NTCE-35, presented at the
AADE National Technical Conference and Exhibition, Houston, Texas, April 12-14, 2011.
3 | P a g e
George, M., Ahmed, R. and Growcock, F. 2012. Stability and Flow Behavior of Fiber-Containing
Drilling Sweeps, Rheology, InTech, Rijeka, Croatia, ISBN: 978-953-51-0187-1,
http://www.intechopen.com/books/rheology/stability-and-flow-behavior-of-fiber-
containing-drilling-sweeps.
Elgaddafi, R., Ahmed, R., George, M. and Growcock, F. 2012. Settling behavior of spherical particles in
fiber-containing drilling fluids, J. Pet. Sci. Eng. (2012), doi:10.1016/j.petrol.2012.01.020.
4 | P a g e
2. Theoretical Study on Stability of Fiber Sweeps
One of the major areas of concerns in the development of fiber sweep technology is fluid instability under
borehole conditions. A recent experimental study (Ahmed and Takach 2008) demonstrated the presence
of fiber separation in low-viscosity sweep fluids. Fiber particle separate or rise in the fluid due to the
buoyant nature of the particles. The separation of the fiber particle substantially reduces the performance
of the sweep fluid.
2.1 Particle Settling Behavior
In contrast to the manufacturing industry, where fiber suspensions are common, the conditions to which
the sweep fluids are subjected can be extremely severe. Modern technological advances within the oil and
gas industry have taken some of the unpredictability out of the well construction phase. Despite this, there
is still no ability to attenuate the harsh environmental conditions that exist within the wellbore, such as
high temperature and high pressure, which necessitate the use of thermally stable, high specific gravity
fluids. These circumstances, unique to the oil and gas industry, and other intangibles, preclude a large
majority of previous work on the flow behavior of homogeneous, non-Brownian suspensions within a
controlled environment. Another dissimilarity is the relative specific gravities of the suspended particles
and the suspending medium. There is a large quantity of experimental, mathematical, and numerical
studies on the settling behavior of spherical and non-spherical particles. However, in the case of fiber
sweeps, the relative gravities are reversed, as the specific gravities of the synthetic fiber and sweep fluid
is less than and greater to water, respectively. This relation encourages buoyancy, and the fibers tend to
rise within the suspension. Despite the opposing directions of motion, the fibers and fiber networks still
exhibit similar general motion and phenomena.
2.1.1 Classification of Particle Settling Behavior
The settling behavior of particles can be divided into four generally accepted classifications, whose
definitions can be revised to reflect the purpose of this study (Scholz 2006):
• Class I: Unhindered settling of discrete particles. The singular particle undergoing this settling
behavior will accelerate until a terminal settling velocity is reached, where the hydrodynamic
drag and gravitational force are balanced. Stokes’ Law is commonly used to describe this motion
of spherical particles.
• Class II: Settling of a dilute suspension of flocculent particles. The randomly moving particles
collide and become entangled, and form aggregates (flocs), which can have increased settling
velocities compared to a single fiber.
• Class III: Hindered and zone settling. Particle concentration is increased to a point where
5 | P a g e
discrete settling no longer occurs. All particles consolidate and displace the liquid phase, which
gives rise to a new upward flow of liquid. This reciprocal motion reduces the overall particle
settling velocity and is called hindered settling. In large surface area settling applications with
high particle concentration, the whole suspension may tend to settle as a “blanket” (zone settling).
• Class IV: Compression settling (compaction and consolidation). As the settling continues, a
compressed layer forms at the bottom of the settling column. As the compression layer is created,
a concentration gradient forms extending upward from the lower sludge region to an increasingly
dilute solids particle concentration.
2.1.2 Motion of Fibrous Particles
Class I and II can be used to describe the motion of synthetic fibers within a low concentrate suspension.
The modeling study considers Class I motion, which simply describes the forces and rising velocity of a
single fiber suspended in a fluid. This prediction can be extrapolated to determine the rising velocity of a
dilute suspension of fiber particles, or Class II motion. Due to the minimal scale of this research, hindered
or zonal settling is readily apparent. While the fibers do rise to the surface of the test cylinders within the
extents of the experiments, there is no true compaction or compression of the fibers at the liquid surface.
The settling motion of a particle is simply a classification of its motion. The settling motion of a fibrous
particle is much more complex (Qi et al. 2011). In the absence of extraneous forces, a sphere settles in a
purely vertical direction. The inconsistent, asymmetrically shaped flexible fiber suspended in a fluid can
exhibit profligate behavior in three dimensions, as well as drift horizontally during its vertical
ascent/descent (Herzhaft and Guazzelli 1999). The rising velocity of these fibers also depends on the fiber
concentration and orientation of the high-aspect ratio particles. Experimental studies investigating dilute
and semi-dilute cylindrical or spheroid particles indicate that concentration is vital in understanding the
settling behavior (Qi et al. 2011; Kuusela et al. 2001, 2003; Koch and Shaqfeh 1989; Herzhaft et al. 1996,
1999). The overall consensus regarding the settling behavior of fiber suspensions was the ability of the
fiber flocs to settle faster than an individual fiber. As the fiber concentration increased, the fibers actually
exhibited hindered settling, and the mean velocity actually decreased below that of a single fiber.
The previous studies mentioned were concerned with phenomena of a similar nature and relevant to this
work. However, due to the particular focus of this study, the ideas and conclusions gathered from
literature must be extrapolated and generalized to correlate to the rising tendency of the fibers. This study
showed rising velocities of fiber particles within a suspension, based on theoretical models and
experimental results.
6 | P a g e
2.2 Modeling Rising Velocity of Particles
The purpose of this modeling study was to predict the behavior of the synthetic monofilament fiber
suspended in fluids with varying rheological properties. In order for the fiber to perform as efficiently and
effectively as possible, the fluid suspending the fiber was engineered to promote the fiber’s wellbore
cleaning capabilities. Thus, a theoretical study was conducted to determine the desirable base fluid
properties and formulate sweep fluids that are stable under borehole conditions.
For the sake of simplicity and to provide easier comparison between fibers oriented perpendicular
(horizontally) and parallel (vertically) to the direction of motion, the analysis only considered a single
fiber suspended in the fluid (Class I settling behavior). This assumption ignored the effect of fiber-fiber
interaction and fiber concentration. The fiber-fiber interaction phenomenon and the fiber concentration in
the fluid were shown to influence the stability of the fiber-fluid system (Ahmed and Takach 2008). This
analysis also addressed two orientations of the fiber: perpendicular to the direction of motion of the fiber
(horizontal) and parallel to the direction of motion of the fiber (vertical). These orientations represent the
boundaries within which the fiber can theoretically orient. However, it has been shown that single settling
fiber will orient itself horizontally (Fan et al. 2004; Kuusela et al. 2001, 2003; Qi et al. 2011). This stable
orientation is also irrespective of fluid velocity, and will eventually return to the horizontal position if
acted upon by an outside force (Qi et al. 2011). Liu and Joseph (1993) investigated how a slender particle
is affected by liquid properties, particle density, length, and shape. They found that only particle
concentration and the end shapes influenced particle orientation during settling. This agrees with studies
by Herzhaft et al. (1996, 1999), which concluded that orientation of a settling spheroid is almost
independent of aspect ratio, but it is correlated to suspension concentration.
As the fiber concentration is increased, the hydrodynamic interactions between the fibers will upset the
stable horizontal fiber. With increasing fiber concentration, the fiber will show greater tendency to orient
parallel toward the direction of motion (Herzhaft et al. 1996; Qi et al. 2011). By analyzing both cases,
we predicted the rheological properties of the base fluid that can keep the fiber in suspension for a
sufficient length of time.
To determine the velocity at which the submerged fiber particles move upward to the surface of the
liquid, the sum of the forces in the vertical direction (y-axis) are set equal to zero. As shown in Fig. 2.1,
the forces acting on the fiber moving within the column of fluid are buoyancy (Fb), hydrodynamic drag
(FD) and gravity (m⋅g). In this case, the fiber is assumed to be oriented horizontally (perpendicular to the
direction of motion of the fiber). The projected surface area of a fiber particle, dependent upon particle
7 | P a g e
orientation, is needed to compute the drag force. In this case, the fiber is horizontally oriented, and the
generalized equation of the force balance in the vertical (y) direction is:
0=−−=∑ mgFFF Dby …………..………………………………...…………………. (2.1)
The forces acting on the fiber are written in terms of their variables.
Thus:
gVAUCgV pphphphDffp ρρρ −− ,2
,,2
1 …...………. (2.2)
where Up,h is the rising velocity of horizontally oriented particle. For
horizontal orientation, the projected area is Ap,h = L x d, and the
volume of the fiber particle Vp = ¼ π d2 L. After inserting the
expressions of projected area and fiber volume and rearranging the
variables, the formula for the rising velocity of the particle is:
2
1
,
,
1
2
−=
hDf
pf
hpC
dgU
ρ
ρρπ………………………………………………...…..…..… (2.3a)
A similar analysis for a vertically oriented particle yields the following rising velocity expression:
2
1
,
,
12
−=
vDf
pf
vpC
LgUρ
ρρ………………...….…………………………...………… (2.3b)
The drag coefficients of the fiber particle must be estimated to predict the rising velocities using the
above equations. Hole cleaning fibers are more or less straight and they can be considered as a long
cylinder for drag force calculation. Drag coefficient correlations and charts for long cylinders are well
documented in the literature. For cylinders oriented perpendicular to the flow (i.e., cross flow), Perry
(1984) presented a chart that can be approximated with the equation given below.
(Re)09.01
(Re)554.09842.0)( ,
Log
LogCLog hD
+
−= ……………….………………………………… (2.4)
FD
mg
Fb
Fig. 2.1 Free body diagram of a cylindrical particle rising in static
fluid
8 | P a g e
This correlation is valid for Reynolds Numbers (Re) ranging from 10-3 to 10. It has been used extensively
in this study, as most lab experiments involving fibers primarily exist in a Reynolds Number range less
than 1.
The drag coefficient of a cylinder oriented in the direction of the flow is only a function of the aspect ratio
(L/d). Based on available data in the literature (Hoerner 1965), the following equation has been developed
to estimate the drag coefficient, CDv:
23.4,
54.1
/1
317.0825.0
+
+=dl
C vD ………………….…….………………………………… (2.5)
As shown in Eqn. (2.4), the drag coefficient of a cylindrical fiber under cross flow condition is a function
of the Reynolds number, which is generally expressed as Re = ρUp,hd/µ (i.e., the ratio of inertial force to
viscous force). This definition holds true for Newtonian fluids, which possess a linear relationship
between shear stress and shear rate. However, the fluids that are often utilized in fiber sweep applications
are non-Newtonian. Hence, the Reynolds Number needs to be redefined using the apparent viscosity
function as Re = ρUp,hd/µapp. The viscosity for Newtonian fluids is an actual property of the fluid, and is
constant despite the shear rate. However, for non-Newtonian fluids, the apparent viscosity varies with
shear rate and rheological parameters of fluid. Applying the Yield Power Law (YPL) rheology model, the
apparent viscosity, µapp, is expressed as:
( ) ( ) 11 −−+= γτγµ &&
y
n
app K ……………………………..…………………….………...…… (2.6)
This study is to determine the desirable Yield Power Law (YPL) fluid properties that must keep the fiber
in suspension in order to create efficient momentum transfer mechanisms between the sweep fluid and
cuttings bed. Hence, only fluids with sufficient yield stress and/or increased low shear rate viscosity can
be utilized to keep the fibers in suspension.
2.3 Non-Rising Particles under Static Conditions
A horizontally oriented cylindrical particle, suspended in YPL fluid (Fig. 2.2), may not rise to the top, but
remain suspended in the fluid depending on the yield stress of the fluid (Dedegil 1987). A static condition
prevails when the forces in the vertical direction acting on the particle are balanced. For a fully suspended
static particle, the momentum balance, Eqn. (2.1) can be rewritten to include the static shear force acting
on the particle in lieu of the drag force that is present under dynamic conditions. By taking a differential
9 | P a g e
element of the cylindrical fiber, the vertical component of the maximum static shear stress (i.e., yield
stress) acting on the fiber can be determined (Fig. 2.2). The direction of the shear stress acting on the
cylinder depends on the location of the differential element as shown in Fig. 2.2. The stress acts on the
area represented by the differential element shown in Fig. 2.3 is expressed as:
θLRddA = ………….………………….………........ (2.7)
Then, the vertical component of the shear force acting on the
differential element is:
θτθθτ sinsin yyshear LRddAdF ⋅=⋅= ……...……. (2.8)
In a fiber oriented vertically and horizontally, shear stresses act on
the circumferential and end areas. However, the end areas are
negligible when compared to circumferential area of the cylinder.
This further simplifies the analysis. Neglecting the forces acting on the cylinder ends, the overall vertical
component of the shear force is subsequently obtained by integrating Eqn. (2.8). After simplification, the
vertical component of the stress force acting on horizontally oriented cylinder becomes:
yhs dLF τ2, = ………….......……………………………………………………...……….. (2.9)
The above equation predicts the maximum value of the
shear force acting on the cylinder. For the sake of
simplicity, the analysis is only concerned with a single
fiber suspended in fluid. The cylinder is considered to
be non-rotating and constantly perpendicular to the
direction of motion of the fiber. In addition, as stated
earlier, the calculations ignore the fiber-fiber
interactions, which will influence the momentum
balance. Writing the force balance in the vertical
direction and replacing the drag force with the shear force in Eqn. (2.1), we get:
gVdLgVF ppyfpy ρτρ −−==∑ 20 ………..………………..…................................. (2.10)
Fig. 2.3 Differential element of a cylinder subject to shear force
Fig. 2.2 Vertical component of shear force acting on a fully
suspended cylinder
10 | P a g e
Replacing the particle volume Vp with πd2L/4, and grouping like terms results in:
( ) 08
2 =
−− ypf
dgdL τρρ
π …………………..…………………………..…………… (2.11)
For a fiber particle oriented in the vertical direction (Fig. 2.4), the shear stress acts vertically along the
length of the fiber particle. By taking a circular differential element of height (dh) and circumference
(πd), the shear force can be written as:
y
L
yvs dLdhdF τπτπ == ∫0, …………….……… (2.12)
Once again rewriting the force balance equation to include the
shear force acting on a vertical oriented particle, and grouping
like terms results in:
( )[ ] 044
=−− ypfdgdL
τρρπ
…...……..……... (2.13)
For this study, the dimensions of the fiber are known and fixed.
Therefore, in order to determine the fluid property that can hold
the fibers is suspension, Eqns. (2.11) and (2.13) must be rewritten
to solve for critical shear stress as a function of density difference
and fiber diameter for a fiber oriented horizontal and vertical, respectively. For a fiber oriented horizontal,
the critical yield stress is:
( )pfhy
dgρρ
πτ −=
8, ……...…… (2.14)
For a vertically oriented fiber particle, the critical
yield stress is calculated as:
( )pfvy
dgρρτ −=
4,
......………….. (2.15)
For this analysis, the fiber size and density are
known. Thus, the critical yield stress is essentially a function of the fluid density, and increases linearly
with density. Figure 2.5 presents the yield stress required to keep a fiber particle with specific gravity of
Fig. 2.5 Critical yield stress as a function of fluid density
for a non-rising particle
ττττy
Fig. 2.4 Shear force acting on a cylinder oriented vertically
11 | P a g e
0.9, length of 10 mm, and diameter of 100 µm vertically oriented. Theoretically, very small yield stress
(less than 1.5 lbf/100 ft2) is needed to keep the fiber in suspension.
2.4 Non-Rising Particles under Dynamic Conditions
The models developed in Section 2.1 are for fiber particles rising in
static fluid. They do not account for other flow phenomena such as
the lateral motion and deformation of the fluid, and hydrodynamic
diffusion effects. Eqns. (2.3) and (2.4) are appropriate for
understanding rising behavior of fibers under static conditions.
However, this study is to determine the hole cleaning efficiency of
the fiber particles in real world situations such as flowing in the
annulus during drillstring rotation. The shearing motion of the fluid in the annulus will affect the apparent
viscosity that subsequently influences the behavior of fiber particles in the base fluid. To model the
behavior of fiber under dynamic conditions accurately, the overall shear rate must be computed from the
primary and secondary flow shear rates. As the sweep fluid is flowing in the annulus, it is subjected to
primary and secondary flows. The primary flow is the gross flow of the fiber-fluid suspension in the
annulus. For a fluid flowing in the annulus, the shear rate varies from zero to its maximum value, which
occurs at the inner wall. Using the narrow slot approximation technique, the shear at any point in the
annulus is given as (Miska 2007):
n
yn dL
dpy
Ky
1
1)(
−
⋅= τγ& ……………………………………………….………..…. (2.16)
Equation (2.16) can be integrated to calculate the average shear rate as:
∫=2/
0
)()2/(
1H
ave WdyyHW
γγ && ……………………………………….…………………… (2.17)
For YPL fluids, due to the presence of the plug zone, the average shear rate (i.e., primary share rate)
calculation procedure is complex. However, the shear rate in plug zone is zero and the average shear rate
is expected to be very low. For Power Law fluid, Eq. (2.17) yields:
( ))/1(
)2/(//1 /1/1
nnW
HdLdpKnnn
primaryave+
== γγ && …………………………………………… (2.18)
W
H
y
Fig. 2.6. Narrow slot representing annulus
12 | P a g e
The width of the slot W = π(do + di)/2 and the clearance H = (do - di)/2. The primary shear rate is a
function of, flow geometry, properties of the fluid and pressure gradient or annular velocity.
The rising motion of the particle induces the secondary flow, which is a function of the fiber particle
rising velocity and the particle diameter:
p
p
ondaryd
U=secγ& ………………………….…………………………..………………..……. (2.19)
Knowing that shear rate is the magnitude of the deformation tensor, the resultant shear rate scalar can be
determined by the Eucledian norm:
2
sec
2
ondaryprimarytotal γγγ &&& += …………………………...…………………………………… (2.20)
2.5 Modeling Results
In order to predict the behavior of the fiber under dynamic
conditions, the annular velocity and hydraulic diameter were
assumed based on conventionally observed values (Table 2.1). For a
dynamic condition, the rising velocity of the fiber particle can be
determined applying the rising velocity equations in combination
with the resultant shear rate. To predict the possible results of the
subsequent bench-top experiments, sensitivity analysis was
conducted using the model. By varying certain properties of the
fluids and determining the resulting rising velocities, the behavior of the fibers in suspension were
investigated. For the sensitivity analysis, the rising velocity of a horizontally oriented fiber was
determined under dynamic conditions varying the yield stress, fluid behavior index “n”, fluid density and
consistency index “K” (Figs. 2.7 to 2.11).
Table 2.1 Input data
Fiber Diameter = 0.0001 m
Fiber Length = 0.01 m
Fiber Density = 897.04 kg/m3
Uannulus = 3.00 ft/sec
= 0.9144 m/sec
Dhydraulic = 3.50 in
= 0.0889 m
K = 1.32 N-sn/m
2
n = 0.52
13 | P a g e
Fig. 2.7a Rising velocity vs. yield stress for horizontally
oriented fiber in 8.33 ppg fluid with n=0.3
Fig. 2.7b Rising velocity vs. yield stress for horizontally
oriented fiber in 8.33 ppg fluid with n=0.6
Fundamental principles of non-Newtonian fluids must be applied in explaining the results presented from
Figs. 2.7 to 2.8. As the consistency index increases, the rising velocity decreases. According to Eqn. (2.6),
the apparent viscosity of the fluid increases when the consistency index is increased. Fibers suspended in
high viscosity fluid experience more resistance to their natural buoyant tendency and decreased rising
velocity. Also apparent in these figures is the merging of floating velocities as the yield stress increases,
regardless of the consistency component. This indicates that as the yield stress of the fluid increases, the
consistency index term in Eqn. (2.6) becomes increasingly irrelevant in determining the Reynolds
Number and rising velocity. It is apparent that the consistency index has marginal effect on the rising
velocity of the fiber.
Fig. 2.8 Rising velocity vs. yield stress for horizontally
oriented fiber in 8.33 ppg fluid with n=1.0
Fig. 2.9 Rising velocity vs. yield stress varying fluid density
for horizontally oriented fiber particle (n = 0.3 and K = 2.1
lbfsn/100 ft
2)
1.0E-10
1.0E-08
1.0E-06
1.0E-04
1.0E-02
0 2 4 6 8 10
Ris
ing
Velo
cit
y (
ft/s
)
Yield Stress (lbf/100 ft2)
n = 0.3 & K = 0.002 to 10.0 lbfsn)/100 ft2
K = 0.002
K = 0.02
K = 0.2
K = 2
K = 10
1.0E-10
1.0E-08
1.0E-06
1.0E-04
1.0E-02
0 2 4 6 8 10
Ris
ing
Velo
cit
y (
ft/s
)
Yield Stress (lbf/100 ft2)
n = 0.6 & K = 0.002 to 10.0 lbfsn)/100 ft2
K = 0.002
K = 0.02
K = 0.2
K = 2
K = 10
1.0E-10
1.0E-08
1.0E-06
1.0E-04
1.0E-02
0 2 4 6 8 10
Ris
ing
Velo
cit
y (
ft/s
)
Yield Stress (lbf/100 ft2)
n = 1.0 & K = 0.002 to 10.0 lbfsn)/100 ft2
K = 0.002
K = 0.02
K = 0.2
K = 2
K = 10
1.0E-10
1.0E-08
1.0E-06
1.0E-04
1.0E-02
0 2 4 6 8 10
Ris
ing
Velo
cit
y (
ft/s
)
Yield Stress (lbf/100 ft2)
Pf =20 ppg
Pf =16 ppg
Pf =12 ppg
Pf = 8.33 ppg
14 | P a g e
Fig. 2.10 Rising velocity vs. yield stress varying fluid
density for horizontally oriented fiber particle (n = 0.6 and K
= 2.1 lbfsn/100 ft
2)
Fig. 2.11 Rising velocity vs. yield stress varying fluid
density for horizontally oriented fiber particle (n = 1.0 and K
= 2.1 lbfsn/100 ft
2)
The yield stress and inherent “n” value of a specific fluid characterizes the degree to which the fluid
behavior is non-Newtonian. Another trend worth investigating from Figs. 2.7 to 2.8 is the relative
closeness of the rising velocity plots for different fluids with respect to their fluid behavior indices. It is
observed that as the fluid behavior index “n” increasingly deviates from unity, the spread of the rising
velocity plots at low yield stress values tends to increase. A careful examination of Figs 2.7 and 2.8
reveals that the increase in the value of “n” substantially increases the rising velocity in fluids with high
“K” values. Even though this is unusual observation, analysis of Eqn. (2.6) shows that, at low shear rates
(i.e., shear rates less than 1 s-1), decreasing the values of “n” results in increased apparent viscosity.
To explore the effect of yield stress on the upward motion of the fiber particles further, the rising velocity
of a horizontal fiber was analyzed varying the yield stress, fluid density and flow behavior index. From
Figs. 2.9 to 2.11, it can be seen that as the density of the fluid increased, the rising velocity increased.
This was attributed to buoyancy; as the fluid became denser than the fiber, the fiber tended to ascend to
the surface faster. This also correlates to the fact that the less dense fluids require smaller yield stresses to
decrease the rising velocity or indefinitely suspend the fibers.
For a vertically oriented fiber particle, the rising velocity strictly relies on the fiber dimensions and
density difference between the particles and the fluid. As shown from Eqn. (2.5), when the fiber particle
orients itself in the direction of motion, the drag coefficient becomes independent of the Reynolds
Number and rheological properties of the fluid. Due to the high aspect ratio and low drag coefficient of
the fiber, the rising velocity of a vertically oriented fiber particle is very high. For a given fiber density,
the rising velocity increases with the increase in mud density (Fig. 2.12). Due to the flexibility of the fiber
and high hydraulic instability, vertical configuration is difficult to maintain; therefore, predicted values do
not reflect the actual rising speeds. In real situations, fibers are not perfectly straight. They also orient
1.0E-10
1.0E-08
1.0E-06
1.0E-04
1.0E-02
0 2 4 6 8 10
Ris
ing
Velo
cit
y (
ft/s
)
Yield Stress (lbf/100 ft2)
Pf =20 ppg
Pf =16 ppg
Pf =12 ppg
Pf = 8.33 ppg
1.0E-10
1.0E-08
1.0E-06
1.0E-04
1.0E-02
0 2 4 6 8 10
Ris
ing
Velo
cit
y (
ft/s
)
Yield Stress (lbf/100 ft2)
Pf =20 ppg
Pf =16 ppg
Pf =12 ppg
Pf = 8.33 ppg
15 | P a g e
randomly under static conditions. Under dynamic conditions, their orientation to some extent is
influenced by the flow field.
2.6 Conclusions
A mathematical model was developed to predict
the rising velocity of fiber particles suspended in
fluid. Sensitivity analysis was undertaken to
examine the effects of fluid properties on the
rising behavior of buoyant fiber particles. The
following conclusions were made based on the
results of the analysis:
• In highly shear-thinning fluids with no
measurable yield stress, the rising
velocity of the fiber was sensitive to the
consistency index (K).
• As the flow behavior index “n” decreased, the fluid became increasingly shear-thinning. The
decrease in “n” allowed for a greater influence of “K” on the rising velocity of the fiber for a
given yield stress.
• Fluid density had a greater magnitude of influence on rising velocity at high yield stress values.
• The model developed for a vertically oriented fiber particle over-predicted the rising velocity,
while the model formulated for a horizontal particle provided reasonable predictions.
Fig. 2.12 Rising velocity vs. mud weight under dynamic
conditions for vertically oriented fiber
0.6
0.8
1.0
1.2
1.4
8 12 16 20
Ris
ing
Velo
cit
y,
Vp
(ft
/sec)
Mud Weight (ppg)
16 | P a g e
Nomenclature
Ap,h = projection area of horizontally oriented
particle
Ap,v = projection area of vertically oriented particle
CD,h = Drag coefficient for a horizontally oriented
particle
CD,v = Drag coefficient for a vertically oriented
particle
d = diameter of fiber particle
di = inner diameter of annulus
do = outer diameter of annulus
Dh = hydraulic diameter (Douter – Dinner)
FB = Buoyancy force
FD = Drag force
g = gravitational acceleration
K = consistency index
L = length of the fiber
m = Mass of a fiber particle
n = flow behavior index
Re = Reynolds Number
R = particle radius (m)
Up,h = rising velocity of particle
Up,h = rising velocity of a horizontally oriented
fiber particle
Up,v = rising velocity of a vertically oriented fiber
particle
W = weight of a fiber particle
VP = volume of a fiber particle
Greek Letters �� = Shear rate
aveγ& = Average shear rate
primaryγ& = Primary shear rate
ondarysecγ& = Secondary shear rate
totalγ& = Total/overall shear rate
µ = fluid viscosity
µapp = Apparent fluid viscosity
θ = Angle
ρf = Fluid density
ρp = Density of a particle
τy = yield stress
τy,h = critical yield stress for a horizontally oriented
particle
τy,h = critical yield stress for a vertically oriented
particle
17 | P a g e
References
Ahmed, R.M. and Takach, N.E. 2008. Fiber Sweeps for Hole Cleaning. Paper SPE 113746 presented at
the Coiled Tubing and Well Intervention Conference and Exhibition, The Woodlands, Texas, 1-2
April. doi: 10.2118/113746.
Dedegil, M.Y. 1987. Drag Coefficient and Settling Velocity of Particles in Non-Newtonian Suspensions.
Journal of Fluids Engineering 109 (3): 319-323.
Fan, L, Mao, Z., and Yang, C. 2004. Experiment on Settling of Slender Particles with Large Aspect Ratio
and Correlation of the Drag Coefficient. Ind. Eng. Chem. Res. 43 (23): 7664-7670.
Herzhaft, B., Guazzelli, E., Mackaplow, M., & Shaqfeh, E. 1996. Experimental Investigation of a
Sedimentation of a Dilute Fiber Suspension. Phys. Rev. Lett. 77 (2): 290-293Hoerner, S. F.
(1965): Fluid-Dynamic Drag. Hoerner Fluid Dynamics, Brick Town, New Jersey.
Herzhaft, B. & Guazzelli, E. 1999. Experimental Study of Sedimentation of Dilute and Semi-Dilute
Suspensions of Fibres. J. Fluid Mech. 384: 133-158Metzner, A.B. and Reed, J.C. 1955. Flow of
Non-Newtonian Fluids – Correlation of the Laminar, Transition, and Turbulent-flow Regions.
A.I.Ch.E. Journal 1 (4): 434-440.
Koch, D. & Shaqfeh, E. 1989. The Instability of a Dispersion of Sedimenting Spheroids. J. Fluid Mech.
209: 521-542.
Kuusela, E., Hofler, K., & Schwarzer, S. 2001. Computation of Particle Settling Speed and Orientation
Distribution in Suspensions of Prolate Spheroids. J. Eng. Math. 41 (2-3): 221-235.
Kuusela, E. & Lahtinen, J. 2003. Collective Effects in Settling of Spheroids Under Steady-State
Sedimentation. Phys. Rev. Lett. 90 (9): 1-4.
Liu, Y.J. & Joseph, D.D. 1993. Sedimentation of Particles in Polymer Solutions. J. Fluid Mech. 255: 565-
595.
Miska, S. 2007. Advanced Drilling, Course Material, University of Tulsa.
Perry, R.H. and Green, D.W. 1984. Perry’s Chemical Engineering Handbook. 6th Edition. Japan:
McGraw-Hill.
Qi, G.Q., Nathan, G.J., & Kelso, R.M. 2011. Aerodynamics of Long Aspect Ratio Fibrous Particles
Under Settling. Paper AJTEC2011-44061 presented at the ASME/JSME 8th Thermal
Engineering Joint Conference, Honolulu, Hawaii, USA, 13-17 March.
Scholz, M. 2006. Wetland Systems to Control Urban Runoff. Amsterdam, The Netherlands: Elsevier.
18 | P a g e
3. Experimental Study on Stability of Fiber Sweeps
The current investigation involved experimental studies of the stability of the fiber in various fluids at
ambient and high temperatures. Several base fluids were chosen to simulate typical drilling and sweep
fluids utilized in the field.
3.1 Scope
The purpose of this investigation was to determine how well various base fluids hold the fiber in
suspension under ambient and high temperature conditions. The fibers had a specific gravity of
approximately 0.9, which was less dense than the typical fluids in which they are suspended. Therefore,
their natural tendency was to rise to the surface of the fluid and form fiber lumps. If the fibers rose while
suspended in the fluid, the hole cleaning performance of the fluid diminished and fiber lumps might plug
some of the downhole tools. As discussed previously, fiber sweep is mainly applied to reduce cuttings in
the wellbore. The fluids utilized for the sweep operations must possess properties conducive to
maintaining a uniform fiber concentration throughout the bulk volume without increasing the ECD.
3.2 Experimental Setup and Procedure
Stability experiments were conducted using 250
ml graduated cylinders. Stand mixers were used
to prepare the test fluid. Test samples were
placed in a laboratory oven to maintain high
temperature conditions. All fluids were
prepared using the same process, unless
otherwise specified by the fluids’ respective
product literature or laboratory preparation
guidelines. Multiple polymeric fluids were
tested, as well as oil-based and synthetic-based
muds. Each polymeric fluid was mixed at
varying concentrations (Table 3.1). The process used for preparing the fluids followed these steps:
Step 1. Preparation of Base Fluid: The fluid samples were initially mixed in bulk using a stand mixer
to begin hydration of the polymer. Hot water was used to accelerate the hydration time. The
polymeric fluids were then placed in a blender, mixed for 30 minutes, and left to sit for 24 hours
to ensure complete hydration.
Step 2. Preparation of Samples: After sitting static for 24 hours, the fluids were re-agitated using a
stand mixer to ensure uniformity of the samples. The bulk fluid was then divided into 300
milliliter (ml) individual samples based on fiber concentration (Fig. 3.1). Fiber was added to the
Table 3.1 Test matrix for stability experiments Weighting Fiber
Agent Concentration
( lb / bbl ) ( lb / bbl )
Xanthan Gum [ XG ] -
( 0.35, 0.87, 1.75, 2.62 ) 8.33 ppg
Polyanionic Cellulose [ PAC ] -
( 0.35, 0.87, 1.75, 2.62 ) 8.33 ppg
XG / PAC [ 1 : 1 ] -
( 0.35, 0.87, 1.75, 2.62 ) 8.33 ppg
Xanthan Gum [ XG ] Barite
( 0.87, 1.75, 2.62 ) 12.1 ppg
PHPA -
( 0.17, 0.35, 0.52 ) 8.33 ppg
Barite
12.2 ppg
Barite
12.1 ppg
OB
M
Mineral Oil-Based 0.00, 0.10, 0.20, 0.30, 0.40
SB
M Internal-Olefin-Based 0.00, 0.10, 0.20, 0.30, 0.40
Base Fluid
W
ate
r-B
ased M
ud [ W
BM
]
0.00, 0.07, 0.14, 0.21, 0.28
0.00, 0.07, 0.14, 0.21, 0.28
0.00, 0.07, 0.14, 0.21, 0.28
0.00, 0.10, 0.20, 0.30, 0.40
0.00, 0.07, 0.14, 0.21, 0.28
19 | P a g e
samples by volumetric concentration in increments of 0.07, 0.14, 0.21, and 0.28 lb/bbl for
unweighted, water-based fluid (approx. 0.02, 0.04, 0.06, and 0.08 percent by weight for 8.33
lb/gal mud).
Step 3. Heating the Samples: The samples were
placed in the oven for approximately 10 minutes
to preheat the fluid. They were removed from
the oven and re-agitated with the stand mixer to
ensure fiber uniformity. The fluid samples were
then immediately transferred to 250 ml
graduated cylinders, and placed in the oven for
one hour.
Step 4. Extracting the Fiber: The graduated cylinders were promptly
removed from the oven after one hour. Under quiescent
conditions, buoyant fiber particles move toward the surface of
the sample increasing the fiber concentration in the upward
direction. In unstable fluids, most of the fiber particles reach the
surface of the sample (Fig. 3.2) after one hour. Using a 60
cubic centimeter (cc) syringe, the top 50 ml of the fluid (Fig.
3.3) were extracted from the cylinders and placed in separate
beakers. Water and surfactant were mixed in with the fiber-
fluid to aid in cleaning the fibers.
Step 5. Weighing the Fiber: The fibers were separated from the fluid
using a screen, and remixed with water and surfactant to further
clean the fibers. The fibers were then screened again, dried in an
oven, and weighed.
3.3 Results
The stability of the fiber-fluid suspension was tested for various fluids at
varying polymer concentration. The results of high temperature (170ºF)
stability experiments are summarized in Table 3.2. Depending on the fluid
type, increasing the polymer concentration may or may not provide
experimental and/or visual evidence of increasing stability. The purpose of
this study was to predict the stability of the fiber sweeps in actual field
conditions. Therefore, all experiments were run at high temperature to
simulate wellbore conditions. For the sake of comparison, a few stability
Fig. 3. 2 Unstable fluids after 1-hour test
Fig. 3. 3 Graduated cylinder used for stability experiment
250 mL
200 mL
2”
8”
Fig. 3.1 Fluid samples
20 | P a g e
experiments were also conducted at ambient temperature.
As discussed previously, the low density of the fiber resulted in a proclivity to rise to the surface. This
was apparent when mixing a small amount of fiber with water, as the fiber almost immediately surfaced.
With all other variables held constant, an increase in fluid density theoretically resulted in a shorter rising
time. Experiments were conducted to test this hypothesis.
3.3.1 Effect of Base Fluid Rheology on Stability of Fiber Sweep
One goal of the research was to determine if the physical
properties of the base fluids influence the stability of the
suspension. The non-Newtonian fluids tested portrayed
non-linear relationships between shear stress and shear
rate. That is, they exhibited an apparent viscosity, a
unique viscosity for an infinitely changing unique shear
rate. For Newtonian fluids, the viscosity defines the
material, since the shear stress or shear rate can be
determined at any point if the viscosity is known.
However, the apparent viscosity cannot define the fluid
because it is ever changing with the flow. Nevertheless,
the apparent viscosity provides a much needed
approximate numerical comparison between the fluids,
as well as a basis for understanding the mechanisms that
provide for a stable fiber-fluid suspension. It is also
important to note that these samples were not subjected
to any shearing motion during the stability portion of the
experiment. This was a static test, and the only shear present was exerted by the fiber itself as it moves
upward in the fluid. The polymers and fluids tested were pseudo plastic, and exhibited shear-thinning
behavior. In other words, the apparent viscosity decreased with increasing shear rate. Relating this to
practical applications, as the fluid circulates through the annulus, it was subjected to varying shear rate.
As the apparent viscosity decreased in response to an increase in shear rate, the ability of the fluid to
maintain stability suffered. For this phase of the investigation, this characteristic was not included in the
analysis.
Multiple stability experiments were conducted at high temperature and a few were conducted at ambient
temperature. Figures 3.4 to 3.14 present the test results along with model predictions. The results are
Table 3.2 One-hour stability of test fluids
Stable Unstable
0.10% XG X
0.25% XG X
0.50% XG X
0.75% XG X
0.10% PAC X
0.25% PAC X
0.50% PAC X
0.75% PAC X
1.20% PAC X
0.10% XG+PAC X
0.25% XG+PAC X
0.50% XG+PAC X
0.75% XG+PAC X
0.25% XG+Barite (12 ppg) X
0.50% XG+Barite (12 ppg) X
0.75% XG+Barite (12 ppg) X
0.25% XG+Barite (16 ppg) X
0.50% XG+Barite (16 ppg) X
0.75% XG+Barite (16 ppg) X
0.05% PHPA X
0.10% PHPA X
0.15% PHPA X
OBM (8.1 ppg) X
OBM (12.2 ppg) X
SBM (7.9 ppg) X
SBM (12.1 ppg) X
Polymer
21 | P a g e
presented in terms of final fiber concentration of the top layer (i.e., the top 50 ml of the 250 ml graduated
cylinder) as a function of initial fiber concentration. The plots show stable and unstable fluid lines. The
unstable fluid line illustrates the maximum fiber concentration that would occur in the top layer if all the
fiber particles migrate into this layer. The stable line shows the initial fiber concentration in the top layer
that does not change with time because of full stability. Results complement the rheological analyses of
these fluids. The fluids that are believed to naturally possess or those that have been designed to have
yield stress generally showed better performance. Xanthan gum (XG), a very common drilling fluid
viscosifier, also used in the food industry due to its yield properties, showed anticipated results (Fig.
3.4a). All except the thinnest fluid (0.10 percent XG) were able to show complete stability. To further test
the stability of Xanthan gum (XCD) based fluids, the test duration was extended to 12 hours (Figs. 3.10
and 3.11). At high temperature, the two thinner fluids showed unstable behavior, but the thicker fluids
were able to retain their yield stress and keep the fibers in suspension. At ambient temperature, there was
no visual or experimental conclusion to show that the fiber had even begun to rise within the fluid.
(a) (b)
Fig. 3.4 One-hour stabilities of XG based fiber sweep at 170°F: a) lab experiments; and b) mathematical model
The polyanionic cellulose (PAC) polymeric fluid showed no stability (Fig. 3.5a). PAC is typically used as
a shale inhibitor - not for its cuttings carrying capacity or for sweeps. However, the solution remains clear
when mixed with water, and is a good tool for observing the fibers in suspension. In an attempt to
determine if the polyanionic cellulose (Polypac R) fluid had any potential as a fiber suspension fluid at
high temperature, the experiment time was shortened to 30 minutes (Fig. 3.13). In this short amount of
test duration, the fiber in the thicker fluid had not yet migrated to the surface, while the thinner fluids
once again showed no stability. As per the experimental results, the PAC fluid mixed at 0.25 percent w/w
showed unexpected stability. Upon visual inspection, the fiber appeared to have grouped in the middle of
the cylinder, preventing the majority of the fiber from rising to the top part of the cylinder. The
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al
Fib
er
Co
nc. (%
)
Initial Fiber Conc. (%)
0.10% XG
0.25% XG
0.50% XG
0.75% XG
Stable
Unstable
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al
Fib
er
Co
nc. (%
)
Initial Fiber Conc. (%)
0.10% XG-Model
0.25% XG-Model
0.50% XG-Model
0.75% XG-Model
Stable
Unstable
22 | P a g e
hydrodynamic and mechanical effects between the container wall and the rising fibers caused the
formation of a fiber plug (lump) that did not move. This bridging created a plug for the lower fibers,
which in turn became entangled. This phenomenon persisted under quiescent condition for the length of
the experiment and subsequent fiber sample removal. After moving the cylinder with the fiber-fluid, the
bridging behavior was overcome, and the fiber-plug rose to the surface in a matter of minutes.
(a) (b)
Fig. 3.5 One-hour stabilities of PAC based fiber sweeps at 170°F: a) lab experiments; and b) mathematical model
(a) (b)
Fig. 3.6 One-hour stabilities of PHPA based fiber sweeps at 170°F: a) lab experiments; and b) mathematical model
Another clear fluid tested during the experiments was Partially-Hydrolyzed Polyacrylamide (PHPA),
which is often utilized as a shale stabilizer in drilling applications. Following the experimental procedure
and mixing at concentrations commonly used in the field, the thickest fluid (0.15 percent PHPA) showed
stable behavior (Fig. 3.6a), while the thin fluid (0.05 percent PHPA) became unstable. The intermediate
viscosity fluid (0.10 percent PHPA) was essentially unstable. At high fiber concentrations, the
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al
Fib
er
Co
nc
. (%
)
Initial Fiber Conc. (%)
0.10% PAC
0.25% PAC
0.50% PAC
0.75% PAC
Stable
Unstable
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al
Fib
er
Co
nc
. (%
)
Initial Fiber Conc. (%)
0.05% PHPA
0.10% PHPA
0.15% PHPA
Stable
Unstable
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al
Fib
er
Co
nc. (%
)
Initial Fiber Conc. (%)
0.10% PAC-Model
0.25% PAC-Model
0.50% PAC-Model
0.75% PAC-Model
Stable
Unstable
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al
Fib
er
Co
nc
. (%
)
Initial Fiber Conc. (%)
0.05% PHPA-Model
0.10% PHPA-Model
0.15% PHPA-Model
Stable
Unstable
23 | P a g e
experimental results showed stable behavior, but this is probably attributable to the formation of fiber
plug (i.e., bridging). In an effort to control the stability of the polymeric fluids, XG and PAC were mixed
at a one-to-one ratio using the same total polymer concentrations as previous tests. (Fig. 3.7a).
Unfortunately, the addition of the XG resulted in an opaque fluid, and visual clues to the mixed fluid’s
stability were impossible. The stability experiment results showed the two thinner fluids to be unstable,
while the two thicker fluids were able to completely hold the fiber in uniform concentration.
Drilling fluids are usually weighted in order to control formation pressure and support the borehole wall.
As the magnitude of difference in specific gravity between the fiber and fluid widens as the fluid density
increases, the fiber is pushed upwards with greater buoyancy force. Figs. 3.8 and 3.9 depict the results of
the weighted fluid stability experiments. Despite the increased buoyancy force acting on the fiber particle,
the experiments showed that the yield stress of the XG fluid prevented the particle from rising. The
weighted and unweighted oil-based mud (OBM) and synthetic-based mud (SBM) demonstrated similar
stability behavior (Fig. 3.9). In these two fluid systems, increasing the density by the addition of barite
had no detrimental effect on the stability of the suspension. The fluids were formulated to provide
properties advantageous to drilling applications. They exhibited relatively low shear stress but had
sufficient yield stress to prevent the fibers from rising.
(a) (b)
Fig. 3.7 One-hour stabilities of XG/PAC based fiber sweeps at 170°F: a) lab experiments; and b) mathematical model
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al F
iber
Co
nc. (%
)
Initial Fiber Conc. (%)
0.10% XG/PAC
0.25% XG/PAC
0.50% XG/PAC
0.75% XG/PAC
Stable
Unstable
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al
Fib
er
Co
nc
. (%
)
Initial Fiber Conc. (%)
0.10% XG/PAC-Model
0.25% XG/PAC-Model
0.50% XG/PAC-Model
0.75% XG/PAC-Model
Stable
Unstable
24 | P a g e
(a) (b)
Fig. 3.8 One-hour stabilities of XG based weighted (12 ppg) fiber sweeps at 170°F:
a) lab experiments; and b) mathematical model
(a) (b)
Fig. 3.9 Measured and predicted one-hour stability of oil-based fluids at 170°F: a) OBM; and b) SBM
Fig. 3.10 Twelve-hour stabilities of XG based fluids at 170°F
Fig. 3.11 Twelve-hour stabilities of XG based fluids at 72°F
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al F
iber
Co
nc.
(%)
Initial Fiber Conc. (%)
0.25% XG-Model
0.50% XG-Model
0.75% XG-Model
Stable
Unstable
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al
Fib
er
Co
nc
. (%
)
Initial Fiber Conc. (%)
8.1 ppg
8.1 ppg-Model
12.2 ppg
12.2 ppg-Model
Stable
Unstable
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al F
iber
Co
nc.
(%)
Initial Fiber Conc. (%)
0.10% XG
0.25% XG
0.50% XG
0.75% XG
Stable
Unstable
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al F
iber
Co
nc.
(%)
Initial Fiber Conc. (%)
0.10% XG
0.25% XG
0.50% XG
0.75% XG
Stable
Unstable
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al
Fib
er
Co
nc
. (%
)
Initial Fiber Conc. (%)
7.9 ppg
7.9 ppg-Model
12.1 ppg
12.1 ppg-Model
Stable
Unstable
25 | P a g e
Intuitively, the magnitude of the fluid’s resistance
to deformation or viscosity should provide a good
indication of its internal ability to resist flow.
Therefore, an increase in a fluid’s viscosity would
result in an increase in the ability to hold particles
in suspension. In relation to this research, an
increase in polymer concentration would result in
higher viscosity, which in turn would yield a more
stable fiber suspension. Visual observation of the
fluids while mixing could also provide insight into
the probable stability. The rheological study on
fibrous fluids that was undertaken previously was
reconciled with the stability experiment results to
compare the apparent viscosities of the stable and
unstable fluids (Figs. 3.14a and 3.14b). Figure
3.14a shows a few low viscosity fluids, some of
which were unstable. This data contradicts the
original hypothesis that the fluid’s viscosity or
rheological properties would determine its ability
to maintain stability. Easily apparent is the
viscosity profile of the 1.20 percent PAC fluid, overall the most viscous fluid present in the figure.
Despite its relatively high viscosity, this fluid was unstable (Fig. 3.14a). In addition, present in this figure
are three stable fluids (0.25 percent XG, 0.50 percent XG/PAC, and 0.15 percent PHPA). It is important
to note that these fluids exhibited lower apparent viscosity at low shear rate than the 1.20 percent PAC
fluid. The 0.25 percent XG fluid even exhibited lower viscosity than the 0.75 percent PAC fluid, which
was also unstable.
Fig. 3.12 One-hour stabilities of PAC based fluids at 72°F
Fig. 3.13 Half-hour stabilities of PAC based fluids at 170°F
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al F
iber
Co
nc. (%
)
Initial Fiber Conc. (%)
0.10% PAC
0.25% PAC
0.50% PAC
0.75% PAC
Stable
Unstable
0.00
0.10
0.20
0.30
0.40
0 0.02 0.04 0.06 0.08 0.1
Fin
al
Fib
er
Co
nc. (%
)
Initial Fiber Conc. (%)
0.10% PAC
0.25% PAC
0.50% PAC
0.75% PAC
Stable
Unstable
26 | P a g e
(a) (b)
Fig. 3.14 Apparent viscosity vs. shear rate of based fluids at 170°F: a) low-viscosity fluids; and b) high-viscosity fluids
In general, XG based fluids showed better stability than other tested polymeric fluids. Xanthan gum
polymer may have structure than can easily tangle with the fiber particles. Figure 3.14b depicts various
stable high-viscosity fluids that were tested. The advantages of the oil-based and synthetic-based mud
become apparent, since they form stable fiber sweeps. Oil-based muds are invert-emulsion. With
dispersed phase (i.e., water phase) ranging from 20 to 30 percent, they exhibit strong structure that can
hinder the movement of fiber particles. Therefore, even though rheological properties play great role in
maintaining the fiber in suspension, other properties of the fluid such as the type of polymer or the
presence of fluid structure may have some influence on the stability of fibrous fluid.
3.3.2 Effect of Temperature on Stability of Fiber Sweep
As stated previously, most of the experiments were carried out at 170°F, recreating the wellbore
environment to the operational extent of the laboratory equipment. A few experiments (Figs. 3.11 and
3.12) were conducted at ambient temperature (72°F) to establish a relationship between temperature and
stability of fiber suspensions. As expected, the suspensions were almost stable under ambient conditions.
In contrast, Figs. 3.10 and 3.5a show the instabilities of thin fluids at high temperature (170°F). This
confirms that the increase in temperature adversely affects the rheological properties of the fluids.
However, this influence declines as the fluids becomes more viscous and increasingly non-Newtonian in
nature.
Xanthan gum-based fluids were stable even under high temperature conditions. To observe instability,
the test duration was extended to 12 hours. Then, thin fluids were able to show instability. When
comparing Fig. 3.12 with Fig. 3.5a, the effect of temperature on the rheological properties of the PAC
1
10
100
1,000
1 10 100 1,000
Ap
pare
nt
Vis
co
sit
y
(cp
)
Shear Rate (s-1)
1.20% PAC 0.75% PAC 0.50% PAC
0.50% XG/PAC 0.25% XG/PAC 0.25% XG
0.15% PHPA10
100
1,000
10,000
1 10 100 1,000
Ap
pare
nt
Vis
co
sit
y
(cp
)
Shear Rate (s-1)
0.50% XG (12 ppg)
0.25% XG (12 ppg)
OBM (12.2 ppg)
SBM (12.1 ppg)
OBM (8.1 ppg)
SBM (7.9 ppg)
27 | P a g e
fluid becomes apparent. While the ambient temperature experiments were able to show favorable results,
increasing the temperature had adverse effects.
3.3.3 Comparison of Model Predictions with Experimental Results
The rising velocity model presented in Section 2 was developed to predict the stability of the fiber
suspension or determine fluid properties necessary to prevent the separation of fiber particles. These
models took into account various forces acting on each individual particle while suspended in the fluid,
such as the buoyancy force created by the difference between fiber and fluid density, and the gravitational
forced exerted on the fiber particle. The model was formulated to predict rising velocities for particles
oriented horizontal and vertical. This was done to simulate the two extreme cases of particle motion
within the fluid. The rheological parameters of the fluids obtained from viscometeric measurements were
inputs into both models to compare model predictions with the actual experimental measurements. As the
tested fluids exhibit non-Newtonian behavior, the rising velocity of the fiber particles becomes a function
of rheological parameters of the fluid. The Yield Power Law (YPL) model is the most accurate
constitutive equation to describe the majority of drilling fluids currently used in the industry. From the
rheological measurements, the parameters of the test fluids were determined using regression analysis and
used in the models. By determining the distance the fiber particles rose in one hour and the amount of
fiber that entered into the top layer in that period, we were able to estimate the final concentrations of the
top layer. Model predictions shown from Figs. 3.4 to 3.9 were obtained using the horizontal orientation
model. These results compared favorably with the test results. Predominately, the predictions were
consistent with the measurements. However, in some cases, discrepancies were substantial. For instance,
PAC based fluids did not show the ability to hold the fiber in suspension, but the model predictions for
highly viscous fluid (0.75 percent PAC) showed some form of intermediate stability at high fiber
concentrations.
The predictions of the vertical orientation model were also compared with measurements, but the results
were very dissimilar. The model predicted all fluids to be unstable. This contradicted the experimental
results, which demonstrated many of the fluids tested to be stable. When comparing the two mathematical
models, the dimensional terms differed. For both models, the area projected to the fluid flow depended on
the orientation of the fiber. If the fiber was oriented perpendicularly, the rectangular profile variables
(length x diameter = 1.0×10-6 m2) were the governing dimensions, and the vertical orientation profile was
the circular end area (¼πd2 = 7.85×10-9 m2). However, this only partially explained the difference. The
drag coefficient (CD) was also present in both equations and was inversely proportional to rising velocity
because it counteracts the buoyancy force.
28 | P a g e
For a vertically oriented particle, drag force resisting the rising fiber is exclusively related to the fiber
aspect ratio (Hoerner 1965) and independent of the fluid properties. Conversely, for a horizontally
oriented particle, the drag force is implicitly related to the Reynolds Number (Perry 1984). The rather
large aspect ratio in comparison to the rectangular projected area and fluid property dependency resulted
in a vertically oriented particle rising velocity anywhere from three to five orders of magnitude greater
than that for horizontally oriented particles.
Fluid density is one of the controllable model parameters that has a marked influence on the stability fiber
sweep. The equation used to determine the rising velocity is a function of the difference between fluid
density and particle density. Mathematically, the rising velocity increases as the difference between the
two densities increases. In theory, an increasingly dense fluid results in a fiber moving upward
instantaneously to the surface. However, the increased viscosity associated with weighted fluid hinders
the barite particles that tend to settle in the fluid under static conditions. For instance, the model
prediction for the stability of the weighted XG based fluids (Fig. 3.8b) shows both favorable and
unfavorable results, while the experimental results indicated stable fluids with a slight departure from
complete uniformity for the two thicker fluids. With its current formulation, the model considers a single
particle rising in the fluid. It does not account for the hindering effect of barite particles. This model will
be improved in the next phase of the project.
The oil-based and synthetic-based muds showed (Fig. 3.9) remarkable stability, both experimentally and
mathematically. After performing the rheological and regression analyses, the weighted and unweighted
fluids for both muds exhibited higher yield stress. All fiber-fluid combinations tested showed stable
behavior. This was reinforced with the mathematical model predictions of similar results.
3.4 Conclusions
This study was undertaken to investigate the stability of fiber sweeps at ambient and high temperature
conditions. Experiments were conducted using different base fluids (water-based and oil-based fluids)
with varying fiber concentrations. Fibers were extracted from the samples after the test and weighed to
determine the final fiber concentration in the top layer. This data was used to determine if the fiber rose
while in the fluid sample, or if uniformity persisted throughout the length of the experiment. These
measurements were compared with stability predictions obtained from the mathematical model. After
analyzing and comparing all the data to date, the following inferences were made:
• Horizontally oriented particle model predictions were in general concurrence with the
experimental data, and reasonable real-time application performance could be predicted using the
29 | P a g e
model. The vertically oriented particle model overestimated rising velocity of fibers in all fluids
tested which did not reflect experimental results, and would not provide accurate predictions.
• Despite the dominant effect of fluid rheology on the stability of fiber sweeps, other properties of
the fluid, such as the type of polymer, the presence of fluid structure, or hindering effect of other
particles, considerably influenced stability.
• Selecting the type of polymer used for drilling sweep applications was critical in designing fluids
that stable under downhole conditions.
• Oil-based and synthetic-based fluids had high fiber stability. This could be attributed to the high
yield stress that they exhibited and the presence of emulsion structure in the two-phase system.
Nomenclature
Up = Particle floating velocity (m/sec)
d = Particle diameter (m)
Dh = Hydraulic diameter (Douter – Dinner)
ECD = Equivalent circulating density
K = Consistency index
n = Fluid behavior index
OBM = Oil-based mud
PAC = Polyanionic cellulose
PHPA = Partially Hydrolyzed Polyacrylamide
SBM = Synthetic-based mud
XG = Xanthan Gum
Greek Letters
µapp = apparent viscosity
τy = yield stress
References
Hoerner, S. F. (1965): Fluid-Dynamic Drag. Hoerner Fluid Dynamics, Brick Town, New Jersey.
Perry, R.H. and Green, D.W. 1984. Perry’s Chemical Engineering Handbook. 6th Edition. Japan:
McGraw-Hill.
30 | P a g e
4. Rheological Properties of Fiber Sweeps
Fiber-containing sweeps (fiber sweeps) are effective tools for wellbore cleaning in horizontal wells. It
has been shown that adding fiber to traditional sweeps can result in an increase in cuttings removal and
reduction in cuttings bed thickness, which reduces the amount of torque and drag in horizontal wells.
Despite some reported successes in the field and favorable research results, the fluid and fiber properties
that define and influence fiber sweep rheology are not fully understood.
The hole-cleaning capabilities of weighted sweeps, high and low viscosity sweeps, and tandem sweeps
are well documented. However, these conventional sweep methods often result in an increase in
equivalent circulating density (ECD). Fiber-containing sweeps, which have promise to overcome this
ECD disadvantage, are becoming popular alternatives. However, little detail is known about the flow and
cuttings-carrying properties of these slurries.
This article presents the rheological measurements carried out on fiber-containing sweep fluids. Tests
were conducted using various unweighted and weighted water-based, mineral oil-based and internal
olefin-based drilling fluids with concentrations of a monofilament synthetic fiber ranging up to 0.4 lb/bbl.
The rheology was measured at ambient and 170ºF. The study shows that fiber concentration has minimal
effect on viscosity, indicating a negligible increase in ECD while providing improved sweep efficiency.
These results can be useful for formulating sweep fluids utilized in deepwater applications.
4.1 Introduction
Poor hole cleaning can lead to an increase in non-productive time and costly drilling problems such as
stuck pipe, premature bit wear, slow rate of penetration, formation fracturing, and high torque and drag
(Ahmed and Takach 2008). A number of field-tested techniques have been introduced over the years to
improve hole cleaning, cuttings transport, and prevent the formation of cuttings beds in the wellbore.
Previous studies indicate that cuttings transport in directional wells is dependent on fluid rheology,
wellbore inclination angle, rotary speed of the drillpipe, flow rate, wellbore geometry, and other drilling
parameters (Valluri et al. 2006). Considering these factors, the most economical and easily employed
procedures involve adding viscosifiers and weighting agents to the drilling fluid to increase the ability of
the fluid to transport cuttings to the surface. In addition, increasing the flow rate has the ability to re-
suspend cuttings, with the maximum pump rate generally provided the best hole cleaning conditions.
However, pressure losses and the equivalent circulating density (ECD) must be considered when
increasing the flow rate. Experience shows that optimal hole cleaning occurs with turbulent flow, but
turbulent flow can erode the filter cake and borewall, as well as increase ECD. Therefore, using laminar
flow at maximum flow rate, paired with fiber sweeps and mechanical agitation such as drillstring rotation
31 | P a g e
and reciprocation, is usually the preferred method for removing cuttings beds (Cameron et al. 2003).
However, these methods often only slow the formation and buildup of cuttings beds and are not very
effective at removing cuttings beds. In response to these problems, drilling fluid sweeps are utilized. The
sweeps remove cuttings that cannot be transported to the surface during normal fluid circulation while
drilling and provide additional vertical lift to the cuttings. Sweeps can be performed in all well
inclinations from vertical to horizontal, as required by wellbore conditions. In deviated, highly inclined,
and extended reach drilling (ERD) wells, sweeps are an essential tool to facilitate wellbore cleaning.
In highly deviated wellbores and especially ERD wells, the cuttings transport performance of a drilling
fluid generally diminishes. Some highly shear-thinning fluids, such as are used in milling operations, are
an exception; even in horizontal wells, the strong viscous coupling between the rotating drill string and
fluid can bring up even metal shavings and fist-sized rock. In highly deviated wellbores, the fluid velocity
has little vertical component, reducing the ability of the drilling fluid to suspend and carry the cuttings.
The increased wellbore length results in higher ECD that limits the flow rate and provides more
opportunity for the cuttings to form a bed on the low side of the wellbore. In addition, the drillpipe rests
on the low side of the wellbore in horizontal sections, forcing the majority of the fluid to the high side and
further encouraging the formation of cuttings beds. Inadequate hole cleaning is common with ERD wells.
Sweeps containing traditional fibrous lost circulation materials (LCM) have been shown to decrease
cuttings and silt beds, as well as reduce torque and drag and improve the rate of penetration (Cameron et
al. 2003). These materials generally refer to organic fibers or plant-derived abrasive substances.
Experimental studies (Ahmed and Takach 2008) and field applications (Bulgachev and Pouget 2006)
have shown that specially designed sweeps containing synthetic monofilament fibers show improved hole
cleaning efficiency over comparable non-fiber sweeps. While these and other cases demonstrate favorable
results when utilizing fiber sweeps, the method for designing these sweeps is still not fully developed.
Visually observing shaker screens to determine whether cuttings transport rate is constant or changing and
plotting these trends versus the sweep volume and fiber concentration are the predominant methods of
monitoring hole-cleaning efficiency.
When fully dispersed in the sweep fluid, fibers form a stable network structure that tends to support
cuttings due to fiber-fiber and fiber-fluid interactions. The fiber-fiber interactions can be by direct
mechanical contact and/or hydrodynamic interference among fiber particles. Mechanical contact among
fibers improves the solids-carrying capacity of the fluid (Ahmed and Takach 2008). Mechanical contact
between the fibers and cuttings beds aid in re-suspending cuttings deposited on the low-side of the
wellbore. As the fibers flow through the annulus, mechanical stresses develop between the settled cuttings
32 | P a g e
and the fibers. These mechanical stresses result in a frictional force that helps to re-suspend the cuttings
while the fiber networks carry the solids to the surface. Also aiding in the solids transport is the fiber-fiber
interaction that enables the fiber network to move as a single phase This fiber network can separate from
the fluid phase. Therefore, at the surface of the cuttings bed the fiber may have a higher velocity than the
fluid phase, which is typically very low. These fast moving fibers can therefore transfer more momentum
to the deposited solids, overcoming the static frictional forces and initiating movement.
This study was undertaken to determine the effect of a fiber on drilling fluid rheology. This
monofilament synthetic material is used in hole-cleaning sweeps throughout the industry. Tests were
conducted of various unweighted and weighted water-based, mineral oil-based and internal olefin-based
drilling fluids with a range of fiber concentrations. The rheology was measured at ambient and 170°F.
The results are expected to be useful for formulating sweep fluids in deviated and deepwater applications.
4.2 Literature Review
Hole-cleaning sweeps may be classified as high-viscosity; high-density; low-viscosity; combinations; and
tandem (Hemphill and Rojas 2002). Factors that govern sweep selection include hole angle, fluid density,
lithology, cuttings diameter, drill pipe rotation, and fracture gradient (Power et al. 2000). In deepwater
and deviated wells, the drilling window between the fracture gradient and pore pressure generally narrows
with increasing depth and hole angle, respectively, reducing the available options for hole cleaning
sweeps. In addition, long horizontal departures are common in order to reduce the environmental impact.
This, combined with the marginal operating window, necessitates a strict adherence to a manageable
ECD. To manage the ECD properly, drilling fluid rheology must be optimized for the conditions, and the
wellbore must be as free of cuttings as possible.
Surface torque and the ability of the rig to overcome it is an important factor when deciding the feasibility
of drilling a well, especially an extended read drilling (ERD) well. The friction generated between the
wellbore and the drillstring in long horizontal sections creates the surface torque. Hole tortuosity in ERD
wells further reduces the ability of the drilling fluid to adequately carry cuttings to the surface. Leaving
cuttings behind adds resistance to the drillstring, which proportionately increases wellbore friction and
surface torque (Maehs et al. 2010). The incorporation of fibrous lost circulation material (LCM) in the
drilling fluid proved a major factor in reducing torque 25 percent on ultra-extended reach wells (Cameron
2001). In drilling an extended reach well in Abu Dhabi, the incorporation of fibrous hole cleaning sweeps
resulted in a dramatic decrease in torque and drag and increased the rate of cuttings return to the surface
by 50 percent (Cameron et al. 2003). While drilling Wytch Farm extended reach wells, it was observed
that the addition of fibrous LCM affected the measurable torque and drag (Robertson et al. 2005). In this
33 | P a g e
case, the LCM was added both to the whole mud system and supplemented with sweeps. It is thought that
the sweeps initiated the decrease in torque, and the LCM in the drilling fluid maintained the reduced
torque levels. The mechanism by which the fibrous LCM decreased the torque was believed to be better
hole cleaning and increased lubricity. The manner in which these mechanisms developed and operated is
not fully understood, but one explanation is that the fibers intertwined to form a mesh, which scoured the
wellbore. The fibers could also have acted as little roller bearings, increasing the lubricity of the
drillstring, further reducing torque (Robertson et al. 2005).
Flexible fibers in suspension form three-dimensional networks that exhibit shear strength and viscoelastic
properties because of the mechanical entanglement. At higher concentrations, the fiber suspension is
capable of supporting a load and transmitting shear stress through the entire flow regime (Swerin 1997).
The mechanical entanglement of the fiber networks can actually hold particles in suspension, preventing
or slowing their segregation. As such, fiber fluid suspensions have also been shown to be an effective
transport mechanism for hydraulic fracturing proppant (Bivins et al. 2005). In fiber free fluids, settling
proceeds according to Stokes’ Law. However, in suspensions with fibers, Stokes’ Law cannot be applied
directly. The sedimentation process may be better characterized as hindered settling. Fibers interfere with
particle settling, generating additional drag, and a distinct liquid-particle boundary does not develop. A
slot test was conducted to evaluate the proppant transport capability and settling prevention property of
the fiber. Proppant in the fiber slurry was stable, and all proppant remained in suspension during the test.
Graphical data showed a decrease in settling velocity of greater than one order of magnitude, as compared
to fluid with no fiber. Furthermore, under the test conditions it was determined that the minimum fluid
viscosity to ensure adequate proppant transport was about 100 cp at 100 s-1 shear rate (Bivins et al. 2005).
The addition of fiber to a fluid also delays the onset of turbulent flow, thus reducing drag and maintaining
the flow in the laminar regime (Gupta et al. 2002). When fibers are added to a shear flow, the fiber
particles orient themselves in the direction of the deformation tensor. This realignment enhances the
fluid’s ability to resist amplification of disturbances. The critical Reynolds Number increases as well as
the general stability of the fluid as the fiber volume fraction and aspect ratio increase (Gupta et al. 2002).
It has also been shown that the presence of fiber or fiber flocs can reduce the intensity of turbulence and
encourage plug flow (Xu and Aidun 2005). This property of fiber-laden fluids is beneficial for hole
cleaning operations as higher pump rates may be used while keeping the fluid in laminar flow. Turbulent
flow while beneficial for wellbore cleaning, can erode the filter cake, resulting in lost circulation or
formation damage.
34 | P a g e
4.3 Fiber Fluid Rheology
Controlling the rheology of the drilling and sweep fluids is essential to maintain favorable wellbore
hydraulics and hole cleaning efficiency. This is of utmost importance when drilling extended and ultra-
extended reach wells in deepwater where the pressure window often requires a minimum overbalanced
wellbore pressure condition. In such environments, the pressure and temperature ranges rise to levels that
are difficult to emulate in laboratory experiments, making it difficult to predict the rheology of the fluids
downhole precisely.
To predict the transport properties and performance of fiber fluid sweeps in downhole conditions, the
basic rheology of the base fluid and suspension must be understood. The proposed formulations for such
fiber sweeps will be most effective when the rheology has been accurately modeled and fine-tuned for
specific wellbore eccentricities. To begin to grasp how the fluid behaves, the relationship between shear
stress and shear rate must be known. This is denoted as the shear viscosity profile, which is an aspect of
the rheology of a fluid that is thought to control laminar flows in pipes, annuli, and other geometries. The
most common shear viscosity models used to characterize non-Newtonian drilling fluids include:
- Bingham-Plastic (BP)
τ = YP + PV·γ
- Power Law (PL)
τ = Kγ
- Yield Power Law (YPL)
τ = τy + Kγn
where τ = shear stress at the wall, γ = shear rate, YP = yield point, PV = plastic viscosity, K = consistency
index, n = fluid behavior index, and τy = yield stress. It will be noted that thixotropic effects like gel
strength are not included in these treatments.
As cuttings carrying capacity is a desirable trait of drilling fluid, a measurable yield stress must be present
to hold the cuttings in suspension. The classic viscosity model used for drilling fluids is the Bingham-
Plastic or pseudoplastic model. Here the shear stress rises linearly with shear rate, with a slope given by
PV. The intercept on the τ axis, YP, is often identified with the carrying capacity of the fluid. Most
drilling fluids exhibit a non-linear shear stress-shear rate relationship, which is best described by the Yield
Power Law model. The YPL model is useful in describing a wide range of polymer-based, oil-based, and
35 | P a g e
synthetic-based drilling fluids, from low shear rate to high shear rate. For fluids with yield stress (τy),
such as the YPL fluid, a certain shear stress must be overcome before flow can initiate. Without yield
stress, the fluid simply follows the Power Law (PL) model. The other two curve-fitting parameters
describe the rheology of PL fluid. K is the viscosity of the fluid at a shear rate of 1.0 s-1, therefore
providing an effective description of fluid viscosity at low shear rates. The flow behavior index, “n”,
indicates the shear-thinning tendency of the fluid. In Newtonian fluids, where viscosity is constant, “n” is
equal to one. Reducing “n” creates a fluid that is shear-thinning, which decreases the effective annular
viscosity and flattens the annular velocity profile, increasing the overall hydraulic efficiency.
Recently, the viscosity profiles of synthetic-based drilling fluids were measured from 80°F to 280°F and
from zero to 5000 psig (Demirdal et al. 2007). The study showed the rheology to be extremely sensitive to
downhole conditions, with the yield stress and consistency index drastically changing with varying
temperature and pressure. The overall trend was that these parameters decreased with increasing
temperature, and increased with increasing pressure. The evaluation also showed that the Yield Power
Law model continued to describe the shear stress-shear rate relationship at all pressure and temperature
conditions. Another study developed a simulator to determine the cuttings transport efficiency of drilling
fluid under high-temperature and high-pressure conditions (up to 200°F and 2,000 psi). The experimental
trend showed that higher temperatures diminished the cleaning efficiency of the fluid (Yu et al. 2007).
Recent experiments studied water-based drilling foam and the effect of temperature on the cuttings
concentration in a horizontal wellbore (Zhu 2005). The results showed that cutting concentration in the
annulus generally increased as the fluid temperature increased.
Previous studies (Demirdal et al. 2007; Yu et al. 2007) show that temperature significantly alters the
viscosity of drilling fluid and ultimately influences the cuttings transport efficiency. As the rheological
properties change, so too does the fluid’s ability to exert viscous and drag forces on the cuttings and the
fiber. As the fluid becomes thinner with elevated temperature, the amount of momentum transferred to the
cuttings is diminished. The thin fluid also loses its ability to maintain a uniform fiber concentration while
flowing in the annulus. This separation decreases the hole cleaning effect of the fiber.
In designing a fiber-fluid formulation for wellbore cleaning sweeps, certain rheological parameters give a
good indication of how well the sweep will perform. The yield stress and yield point of the fluid represent
the amount of force required to move the fluid. At the same time, if the fluid possesses adequate yield
stress to prevent the natural buoyancy of the fiber, the fiber will not separate. The yield stress indicates
how well the sweep will maintain uniformity when circulating up the annulus.
36 | P a g e
4.4 Experimental Investigations
The current investigation involves experimental studies of the rheology of fiber-containing sweep fluids.
Several base fluids were chosen to simulate the various drilling and sweep fluids utilized in the field
(Table 4.1). A specially processed 100 percent virgin synthetic monofilament fiber was supplied for this
research (Table 4.2), and was mixed with the base fluids at varying concentrations.
Table 4.1 Test matrix of rotational viscometer measurements
Table 4.2 Fiber properties
The water-based fluids included fluids prepared with xanthan gum (XCD) at two mud weights,
polyanionic cellulose (Polypac R ), xanthan gum (XG), partially hydrolyzed polyacrylamide (PHPA) and
mixtures of XG and PAC. Formulations were prepared with a broad range of concentrations of these
polymers. Also tested were weighted mineral oil-based and internal olefin-based drilling fluids.
4.4.1 Experimental Setup
The shear viscosity experiments were conducted using stand mixers (Fig. 4.1), rotational viscometers
(Chandler 35 and Fann 35A, Fig. 4.2), thermocup, mud balance, and a laboratory oven. The Chandler 35
rotational viscometer has 12 speeds and was modified to include a 1/5 spring. The weaker spring allowed
for more sensitive and accurate measurements in the low shear rate range and reported all dial readings at
five times (5x) higher than actuality. Both viscometers were calibrated and tested using multiple fluids of
varying viscosities to ensure that readings were comparable.
Base Weighting Fiber
Fluid Agent Concentration( lb / bbl ) ( lb / bbl )
XG None
( 0.35, 0.87, 1.75, 2.62 ) 8.33 ppg
PAC None
( 0.35, 0.87, 1.75, 2.62 ) 8.33 ppg
XG / PAC [ 50%/50% ] None
( 0.35, 0.87, 1.75, 2.62 ) 8.33 ppg
XG Barite
( 0.87, 1.75, 2.62 ) 12.1 ppg
PHPA None
( 0.17, 0.35, 0.52 ) 8.33 ppg
Mineral Oil-base Barite
[ VERSACLEAN® System ] 12.2 ppg
Internal-Olefin-base Barite
[ NOVAPLUS® System ] 12.1 ppgSB
M
0.00, 0.20, 0.40
OB
M
0.00, 0.14, 0.28
0.00, 0.20, 0.40
0.00, 0.14, 0.28
0.00, 0.14, 0.28
0.00, 0.14, 0.28
0.00, 0.20, 0.40
Wate
r-B
ased M
ud [ W
BM
]
Material = Polypropylene
Spec. Grav. = 0.91
Length = 0.40 in (10 mm)
Diameter = 0.004 in (100 μm)
Melting Point = 325°F – 350°F
Fig. 4.1 Stand mixers
4.4.2 Test Procedure
The steps required to prepare the samples and
Step 1. Preparation of Base Fluid:
and barite. Immediately after mixing, all water
a minimum of 24 hours to ensure full hydration. The fluids were then re
sample was obtained to determine the specific gravity using
Step 2. Preparation of Samples: After fluids were mixed and hydrated (if necessary), individual samples
were weighed and organized according to the polymer and fiber concentration. Fiber was added to
the samples at weight concentrations of 0.02,
water-based fluids, 0.08 percent
based and non-aqueous fluids it corresponded to 0.4 lb/bbl fiber.
Step 3. Viscometer Measurements at Ambient Tempera
rheologies of the base fluids were measured using two rotational viscometers (Chan
Fann 35A). If the viscosity of the fluid being measured exceeded the spring capacity of the
Chandler 35, the less sensitive but
measurements.
Step 4. Viscometer Measurements at High Temperature:
The oven was set at approximately 180°F, and samples were agitated every 15
uniformity. Once a sample was heated to 170°F as confirmed by a mercury thermometer, the
Fig. 4.2 Rotational viscometers
The steps required to prepare the samples and record measurements are as follows:
Preparation of Base Fluid: Bulk base fluid samples were prepared by mixing water, viscosifiers
and barite. Immediately after mixing, all water-based fluids were covered and left undisturbed for
a minimum of 24 hours to ensure full hydration. The fluids were then re-agitated, and a uniform
sample was obtained to determine the specific gravity using the mud balance.
After fluids were mixed and hydrated (if necessary), individual samples
were weighed and organized according to the polymer and fiber concentration. Fiber was added to
the samples at weight concentrations of 0.02, 0.04, 0.06, and 0.08 percent. For the unweighted
percent corresponded to 0.28 lb/bbl fiber, whereas for the 12
aqueous fluids it corresponded to 0.4 lb/bbl fiber.
Viscometer Measurements at Ambient Temperature: After all samples were prepared, the
rheologies of the base fluids were measured using two rotational viscometers (Chan
Fann 35A). If the viscosity of the fluid being measured exceeded the spring capacity of the
tive but larger range Fann 35A was utilized for the higher shear rate
Viscometer Measurements at High Temperature: Samples were placed in an oven for heating.
The oven was set at approximately 180°F, and samples were agitated every 15
uniformity. Once a sample was heated to 170°F as confirmed by a mercury thermometer, the
37 | P a g e
2 Rotational viscometers
Bulk base fluid samples were prepared by mixing water, viscosifiers,
based fluids were covered and left undisturbed for
agitated, and a uniform
After fluids were mixed and hydrated (if necessary), individual samples
were weighed and organized according to the polymer and fiber concentration. Fiber was added to
. For the unweighted
corresponded to 0.28 lb/bbl fiber, whereas for the 12-ppg water-
After all samples were prepared, the
rheologies of the base fluids were measured using two rotational viscometers (Chandler 35 and
Fann 35A). If the viscosity of the fluid being measured exceeded the spring capacity of the
Fann 35A was utilized for the higher shear rate
Samples were placed in an oven for heating.
The oven was set at approximately 180°F, and samples were agitated every 15 minutes to ensure
uniformity. Once a sample was heated to 170°F as confirmed by a mercury thermometer, the
38 | P a g e
sample was removed from the oven and mixed for 30 seconds using a stand mixer. This mixing
time was deemed adequate to achieve uniform re-dispersion of the fibers. Immediately after
mixing, a portion of the sample was poured into the thermocup. Using a mercury thermometer, the
thermocup temperature was adjusted to achieve a constant fluid temperature of 170°F. The
viscometer measurements were taken using the procedure described in Step 3.
4.5 Experimental Results
The shear stress of each fluid was measured from 1 rpm to 600 rpm at ambient and elevated temperature.
When circulating through the annulus, most parts of the fiber sweep are in the plug flow regime.
Therefore, the low shear rate range is more significant when analyzing and predicting the behavior of
these fiber sweeps under downhole conditions. However, to provide a general understanding of fiber
sweeps, Figs. 4.3 to 4.8 show the results of the viscometer measurements for the entire shear rate range.
Experiments were conducted with four (4) increasing levels of fiber concentration (Step 2). For the
majority of the fluids tested, the trends were consistent as fiber concentration increased. To reduce data
clutter, only the intermediate (0.14 lb/bbl) and high (0.28 lb/bbl) fiber concentrations were included in the
figures for the water-based drilling fluids.
4.5.1 Effect of Fiber Concentration
One goal of the research was to determine the effect that adding fiber and increasing the fiber
concentration has on the rheology of the fluid. As it has been shown in previous studies (Ahmed and
Takach 2008), adding fiber to fluid has an insignificant effect on the flow behavior of the fluid.
According to field results and supporting theories stated previously, adding fiber to the fluid may actually
improve the hole cleaning performance without affecting the rheological properties of the fluid. After
analyzing the results of the viscometer experiments, we found that the fiber had no predictable influence
on the fluid rheology. In most cases, the addition of fiber to the base fluid resulted in a slight increase in
shear stress (Figs. 4.4a, 4.5c, 4.7b). Other times, the base fluid exhibited a higher shear stress than the
fiber fluid (Fig. 4.6c). Despite these deviations from the base fluid, the magnitude of their departure from
the baseline was relatively insignificant. Careful observation of these figures shows that at shear rates less
than 10 s-1, the shear stress values for the majority of the figures were almost identical (Figs. 4.6c and
4.7b).
In another case, two similar polymeric fluids showed contradicting trends. The high-temperature,
weighted fiber fluid mixed with 0.87 lb/bbl XG polymer (Fig. 4.6a) showed the most common
characteristic, with the shear stress increasing with fiber concentration. This was apparent in the low
shear rate range, but the fiber concentration lost influence in the higher shear rate range. Conversely, the
39 | P a g e
high-temperature, weighted fiber fluid mixed with 1.75 lb/bbl XG mud (Fig. 4.6b) indicated an opposing
trend, with fiber concentration reducing shear stress throughout the shear rate range measured. Despite
this peculiarity, the change in shear stress in the region of interest (low shear rate) was of little
consequence. At the shear rate 51.09 s-1, the difference in shear stress between the base fluid and 0.4
lb/bbl fiber fluid (Fig. 4.6a) was 15 percent.
(a)
(b)
(c)
(d)
Fig. 4.3 Rheology of XG based fluid at 72°F and 170°F varying fiber and polymer concentrations:
a) 0.35 lb/bbl XG; b) 0.87 lb/bbl XG; c) 1.75 lb/bbl XG; and d) 2.62 lb/bbl XG
0.1
1
10
1 10 100 1000
Sh
ea
r S
tre
ss
(lb
f/10
0 f
t2)
Shear Rate (s-1)
1
10
100
1 10 100 1000
Sh
ea
r S
tres
s (
lbf/
100
ft2
)
Shear Rate (s-1)
x Base Fluid, 72°F + 0.14 lb/bbl, 72°F ○ 0.28 lb/bbl, 72°F ж Base Fluid, 170°F ∆ 0.14 lb/bbl, 170°F □ 0.28 lb/bbl, 170°F
Fiber Concentration
0.1
1
10
100
1 10 100 1000
Sh
ea
r S
tres
s (
lbf/
10
0 f
t2)
Shear Rate (s-1)
1
10
100
1 10 100 1000
Sh
ea
r S
tres
s (
lbf/
10
0 f
t2)
Shear Rate (s-1)
40 | P a g e
(a)
(b)
(c)
(d)
Fig. 4.4 Rheology of PAC based fluid at 72°F and 170°F varying fiber and polymer concentrations:
a) 0.35 lb/bbl PAC; b) 0.87 lb/bbl PAC; c) 1.75 lb/bbl PAC; and d) 2.62 lb/bbl PAC
Another important point was the remarkably minor influence that fiber concentration has on shear stress
in the oil-based and synthetic-based muds. Even at low shear rates, the change in shear stress ranged from
4 to 6 percent for most cases, with the extreme difference of 8.8 percent at 51 s-1 (Fig. 4.8a). This finding
is encouraging, as fiber can be added to sweeps to enhance hole cleaning without fear of increasing the
ECD. Oil-based and synthetic-based muds are often used in harsh, not-easily accessible environments
where there is concern for shale interaction and environmental impact. These well locations often require
high-angle wells to reduce the footprint and target multiple formations. Fiber sweeps may be employed to
0.1
1
10
1 10 100 1000
Sh
ear
Str
ess
(lb
f/1
00
ft2
)
Shear Rate (s-1)
0.1
1
10
100
1 10 100 1000
Sh
ear
Str
ess
(lb
f/10
0 f
t2)
Shear Rate (s-1)
x Base Fluid, 72°F + 0.14 lb/bbl, 72°F ○ 0.28 lb/bbl, 72°F ж Base Fluid, 170°F ∆ 0.14 lb/bbl, 170°F □ 0.28 lb/bbl, 170°F
Fiber Concentration
0.1
1
10
100
1 10 100 1000
Sh
ea
r S
tres
s (
lbf/
100
ft2
)
Shear Rate (s-1)
0.1
1
10
100
1 10 100 1000
Sh
ea
r S
tress
(lb
f/10
0 f
t2)
Shear Rate (s-1)
41 | P a g e
reduce the cuttings beds in these extended reach horizontal wells in which pressure loss along the annulus
is a major concern.
In every case, the addition of fluid had no impact on the general shape of the shear stress versus shear rate
plots. The approximate model for the base fluid accurately described the behavior of the fiber fluid, at
ambient and high temperature.
(a)
(b)
(c)
(d)
Fig. 4.5 Rheology of XG/PAC (50%/50%) mix fluid at 72°F and 170°F varying fiber and polymer concentrations:
a) 0.35 lb/bbl XG/PAC; b) 0.87 lb/bbl XG/PAC; c) 1.75 lb/bbl XG/PAC; and d) 2.62 lb/bbl XG/PAC
0.1
1
10
1 10 100 1000
Sh
ear
Str
es
s (
lbf/
100
ft2
)
Shear Rate (s-1)
0.1
1
10
100
1 10 100 1000
Sh
ear
Str
ess
(lb
f/1
00 f
t2)
Shear Rate (s-1)
x Base Fluid, 72°F + 0.14 lb/bbl, 72°F ○ 0.28 lb/bbl, 72°F ж Base Fluid, 170°F ∆ 0.14 lb/bbl, 170°F □ 0.28 lb/bbl, 170°F
Fiber Concentration
0.1
1
10
100
1 10 100 1000
Sh
ear
Str
ess
(lb
f/1
00 f
t2)
Shear Rate (s-1)
0.1
1
10
100
1 10 100 1000
Sh
ear
Str
ess
(lb
f/10
0 f
t2)
Shear Rate (s-1)
42 | P a g e
(a)
(b)
(c)
Fig. 4.6 Rheology of XG based weighted fluids (12 ppg) at 72°F and 170°F varying fiber and polymer concentrations:
a) 0.87 lb/bbl XG; b) 1.75 lb/bbl XG; and c) 2.62 lb/bbl XG
In a study conducted by Ahmed and Takach (2008), the hole-cleaning efficiency of fiber sweeps was
compared to base fluid (viscous) sweeps. The experiments were carried out in a flow loop with varying
inclination angles, measuring the cuttings bed height and frictional pressure loss during sweep circulation.
For the same annular velocity, the fiber sweeps generally showed a reduced bed height in the flow loop
annulus. Annular pressure loss was recorded as a function of time for various flow rates. The results
indicated that frictional pressure loss was approximately equal for the base fluid and fiber sweep. In one
instance, the fiber sweep pressure loss was less than that exhibited by the base fluid. Pipe viscometer
experiments were also conducted comparing flow curves of the base fluid and fiber sweep. Viscometer
1
10
100
1 10 100 1000
Sh
ea
r S
tre
ss
(lb
f/1
00
ft2
)
Shear Rate (s-1)
10
100
1000
1 10 100 1000
Sh
ear
Str
ess
(lb
f/10
0 f
t2)
Shear Rate (s-1)
x Base Fluid, 72°F + 0.20 lb/bbl, 72°F ○ 0.40 lb/bbl, 72°F ж Base Fluid, 170°F ∆ 0.20 lb/bbl, 170°F □ 0.40 lb/bbl, 170°F
Fiber Concentration
1
10
100
1 10 100 1000
Sh
ea
r S
tress
(lb
f/10
0 f
t2)
Shear Rate (s-1)
43 | P a g e
pressure loss was measured as a function of flow rate. At low flow rates (laminar, plug flow regime),
pressure loss for the base fluid and fiber sweep were equal and the flow curves were similar. A similar
conclusion was drawn from a previous study (Xu and Aidun 2005) comparing velocity profiles as a
function of fiber concentration. The inclusion of a small amount of fiber had minimal effect on the
velocity profile at low Reynolds Number flow.
(a)
(b)
(c)
Fig. 4.7 Rheology of PHPA based fluids at 72°F and 170°F varying fiber and polymer concentrations:
a) 0.17 lb/bbl PHPA; b) 0.35 lb/bbl PHPA; and c) 0.52 lb/bbl PHPA
0.1
1
10
1 10 100 1000
Sh
ear
Str
ess
(lb
f/1
00
ft2
)
Shear Rate (s-1)
1
10
100
1 10 100 1000
Sh
ear
Str
ess
(lb
f/10
0 f
t2)
Shear Rate (s-1)
x Base Fluid, 72°F + 0.14 lb/bbl, 72°F ○ 0.28 lb/bbl, 72°F ж Base Fluid, 170°F ∆ 0.14 lb/bbl, 170°F □ 0.28 lb/bbl, 170°F
Fiber Concentration
0.1
1
10
100
1 10 100 1000
Sh
ea
r S
tres
s (
lbf/
10
0 f
t2)
Shear Rate (s-1)
44 | P a g e
4.5.2 Effect of Temperature
In order to reproduce the behavior of the fiber fluid under downhole conditions, the ambient temperature
experiments were repeated at high temperature, as shown from Fig. 4.3 to Fig. 4.8. The general trend
exhibited in all the fluids studied was that the fluid’s ability to flow increases with temperature. The
warmer temperatures created a “thin” fluid that was more easily deformed. This enhanced tendency for
deformation diminished the fluid’s ability to project its inherent flow resistance.
Ann important trend became apparent when analyzing temperature influence on viscosity at different
fiber concentrations. As mentioned previously, adding fiber or increasing fiber concentration showed a
general tendency for slightly higher viscosity measurements at ambient temperature when compared to
the base fluid. In most cases, this same trend was observed in the high-temperature measurements (Figs.
4.5c and 4.5d). However, in some fluids, the increased temperature nullified the influence of fiber
concentration (Fig. 4.3b). In these instances, adding fiber to the fluid resulted in an increase in viscosity
at ambient temperature. However, when taking measurements of the same fluid at high temperature the
fiber showed little or no influence on the viscosity.
(a)
(b)
Fig. 4.8 Rheology of weighted (12.2 ppg) oil-based fluids at 72°F and 170°F varying fiber concentrations:
a) OBM; and b) SBM
The oil-based and synthetic-based muds showed remarkable performance at ambient and high
temperature. Regardless of temperature, fiber had an insignificant influence on viscometric
measurements. Throughout the entire shear rate range, the percentage difference between base fluid and
fiber fluid remained low and relatively constant. None of the water-based fluids tested showed this level
1
10
100
1 10 100 1000
Sh
ear
Str
es
s (
lbf/
10
0 f
t2)
Shear Rate (s-1)
x Base Fluid, 72°F + 0.20 lb/bbl, 72°F ○ 0.40 lb/bbl, 72°F ж Base Fluid, 170°F ∆ 0.20 lb/bbl, 170°F □ 0.40 lb/bbl, 170°F
Fiber Concentration
1
10
100
1 10 100 1000
Sh
ear
Str
es
s (
lbf/
100
ft2
)
Shear Rate (s-1)
45 | P a g e
of control over the entire shear rate range at both temperatures.
The temperature of the fluids was altered to provide a closer representation to actual downhole conditions.
However, elevated pressure conditions in the wellbore were not considered in this study, partly as a
consequence of the operational capability of the equipment available for these experiments. Previous
studies investigated the effect of elevated pressure on the rheology of various fluids. Zhou et al. (2004)
conducted experiments to investigate aerated mud cuttings transport in an HPHT flow loop. The effect of
elevated pressure (up to 500 psi) was found to have minimal influence on cuttings concentration.
Another study (Alderman et al. 1988) investigated the influence of high temperature and high pressure on
water-based mud. The viscous behavior of the fluids in the HPHT conditions reflected the characteristics
of their respective continuous phases: a weak pressure dependence and an exponential temperature
dependence. It was also shown that the fluid yield stress was essentially independent of pressure, but
highly influenced by temperature. Other studies concentrating on the pressure and temperature effects on
cement slurry rheology gave similar results. The plastic viscosity of the cement slurry showed little
increase with increasing pressure (up to 5000 psi) in relation to the significant effect of increased
temperature up to 260°F (Ravi and Sutton 1990).
4.5.3 Shear Viscosity Parameters
The first step in analyzing the fiber fluid shear viscosity was to record all the viscometer shear stress
measurements. Least-square regression was performed to determine the rheological parameters for all
fluid-fiber-temperature formulations (Tables 4.3 through 4.8). The coefficient of determination, R2,
represents how well the measured shear stress values correlate with the values predicted by the Yield
Power Law model. An R2 value of 1.00 represents an exact match of experimental data with the
predictive model data. The vast majority of the experimental data points fit the regression model
extremely well.
46 | P a g e
Table 4.3 Rheological parameters of XG based fluid with varying fiber concentration at 72°F and 170°F
As discussed previously, the shear viscosity models are mathematical relations that approximately
represent the measured data using curve-fitting parameters. Some properties believed to exist in some
polymers do not always manifest themselves. For instance, XG fluids typically exhibit a yield stress only
at high concentrations. In our study, at low concentrations XG fluids best fit the regular Power Law
model without a yield stress. This yield stress value increased as polymer concentration increases and the
fluid became more viscous at low temperature (Table 4.3). However, at high temperature (170°F) even
the higher concentration fluids did not show a yield stress value. Regardless, neither PAC (Table 4.4) nor
PHPA (Table 4.7), by contrast, was anticipated to show a yield stress. Indeed that was the case, except
for a couple of PHPA cases. However, the uncertainty in the yield stress in all of these cases can be
expected to be approximately 1 lb/100 ft2.
Table 4.4 Rheological parameters of PAC based fluid with varying fiber concentration at 72°F and 170°F
τy k n R2τy k n R2
lbf /100 ft2 lbf-sn/100 ft2 lbf /100 ft2 lbf-sn/100 ft2
0.00 0 0.04 0.76 1.00 0 0.09 0.61 0.99
0.14 0 0.08 0.65 0.99 0 0.06 0.68 1.00
0.28 0 0.08 0.65 0.99 0 0.06 0.67 0.99
0.00 0 0.80 0.48 1.00 0 0.34 0.53 1.00
0.14 0 0.75 0.50 1.00 0 0.34 0.54 1.00
0.28 0 0.77 0.50 1.00 0 0.40 0.51 1.00
0.00 4.75 5.06 0.33 1.00 0 4.41 0.31 1.00
0.14 6.24 4.38 0.35 1.00 0 2.69 0.36 0.99
0.28 6.34 4.27 0.36 1.00 0 4.03 0.32 1.00
0.00 13.33 8.76 0.31 1.00 0 10.83 0.25 1.00
0.14 14.33 8.97 0.31 1.00 0 9.04 0.28 1.00
0.28 16.15 8.08 0.33 1.00 0 10.43 0.25 1.00
Rheological Properties
72°F 170°FComposition
XG
1.75 lb/bbl
XG
2.62 lb/bbl
FluidFiber Conc.
( lb / bbl )
XG
0.35 lb/bbl
XG
0.87 lb/bbl
τy k n R2τy k n R2
lbf /100 ft2 lbf-sn/100 ft2 lbf /100 ft2 lbf-sn/100 ft2
0.00 0 0.03 0.84 0.99 0 0.05 0.61 0.97
0.14 0 0.03 0.85 0.99 0 0.06 0.60 0.99
0.28 0 0.04 0.77 0.99 0 0.08 0.57 0.98
0.00 0 0.09 0.82 1.00 0 0.02 0.92 0.99
0.14 0 0.10 0.82 1.00 0 0.04 0.84 0.99
0.28 0 0.11 0.81 1.00 0 0.04 0.85 0.99
0.00 0 0.44 0.74 1.00 0 0.16 0.77 1.00
0.14 0 0.56 0.70 1.00 0 0.15 0.78 1.00
0.28 0 0.61 0.69 1.00 0 0.15 0.78 1.00
0.00 0 1.22 0.68 0.99 0 0.28 0.76 1.00
0.14 0 1.36 0.67 0.99 0 0.32 0.75 1.00
0.28 0 1.52 0.65 0.99 0 0.27 0.79 1.00
72°F
Rheological Properties
170°F
FluidFiber Conc.
( lb / bbl )
Composition
PAC
0.35 lb/bbl
PAC
0.87 lb/bbl
PAC
1.75 lb/bbl
PAC
2.62 lb/bbl
47 | P a g e
Table 4.5 Rheological parameters of XG/PAC (50%/50%) based fluid with varying fiber concentration at 72°F and 170°F
Table 4.6 Rheological parameters of XG+Barite (12 ppg) based fluid with varying fiber concentration at 72°F and 170°F
Table 4.7 Rheological parameters of PHPA based fluid with varying fiber concentration at 72°F and 170°F
Table 4.8 Rheological parameters of OBM and SBM with varying fiber concentration at 72°F and 170°F
τy k n R2 τy k n R
2
lbf /100 ft2 lbf-sn/100 ft2 lbf /100 ft2 lbf-sn/100 ft2
0.00 0 0.05 0.71 0.98 0 0.06 0.60 0.97
0.14 0 0.05 0.72 0.99 0 0.06 0.60 0.97
0.28 0 0.05 0.74 0.99 0 0.05 0.62 0.97
0.00 0 0.19 0.69 1.00 0 0.08 0.66 0.99
0.14 0 0.25 0.65 1.00 0 0.07 0.71 0.99
0.28 0 0.29 0.63 1.00 0 0.08 0.71 1.00
0.00 0 0.66 0.62 1.00 0 0.38 0.66 1.00
0.14 0 0.98 0.56 1.00 0 0.53 0.62 1.00
0.28 0 0.98 0.57 1.00 0 0.66 0.59 1.00
0.00 0 2.17 0.53 0.99 0 0.61 0.64 1.00
0.14 0 2.48 0.51 1.00 0 1.09 0.56 1.00
0.28 0 2.64 0.50 1.00 0 1.36 0.53 1.00
Composition170°F72°F
Rheological Properties
XG/PAC
0.35 lb/bbl
XG/PAC
0.87 lb/bbl
XG/PAC
1.75 lb/bbl
XG/PAC
2.62 lb/bbl
FluidFiber Conc.
( lb / bbl )
τy k n R2τy k n R2
lbf /100 ft2 lbf-sn/100 ft2 lbf /100 ft2 lbf-sn/100 ft2
XG+Barite 0.00 0.52 0.55 0.62 0.99 0 1.05 0.46 0.99
0.87 lb/bbl 0.20 0.84 0.50 0.64 1.00 0 0.95 0.47 0.99
12 ppg 0.40 1.09 0.77 0.58 0.99 0 1.07 0.46 0.99
XG+Barite 0.00 7.06 4.23 0.45 0.99 3.48 5.78 0.34 0.99
1.75 lb/bbl 0.20 8.02 4.07 0.46 1.00 3.64 5.78 0.32 0.99
12 ppg 0.40 9.20 3.91 0.46 1.00 1.07 6.93 0.29 1.00
XG+Barite 0.00 16.91 10.14 0.36 1.00 7.64 16.37 0.22 1.00
2.62 lb/bbl 0.20 17.03 10.31 0.36 1.00 9.59 13.35 0.24 0.99
12 ppg 0.40 17.09 10.25 0.36 1.00 6.64 15.07 0.23 0.99
72°F
Rheological Properties
170°F
FluidFiber Conc.
( lb / bbl )
Composition
τy k n R2τy k n R2
lbf /100 ft2 lbf-sn/100 ft2 lbf /100 ft2 lbf-sn/100 ft2
0.00 0 0.17 0.55 0.99 0 0.06 0.56 0.99
0.14 0 0.16 0.56 0.99 0 0.06 0.56 0.99
0.28 0 0.10 0.64 0.99 0 0.07 0.55 0.99
0.00 0 0.34 0.54 1.00 0 0.30 0.47 1.00
0.14 0 0.31 0.56 1.00 0 0.35 0.45 1.00
0.28 0.51 0.22 0.62 1.00 0 0.38 0.45 0.99
0.00 1.05 0.40 0.58 1.00 0 0.59 0.44 1.00
0.14 1.07 0.46 0.56 1.00 0 0.61 0.43 1.00
0.28 0 0.61 0.69 0.99 0 0.72 0.42 1.00
PHPA
0.17 lb/bbl
72°F 170°FComposition
FluidFiber Conc.
( lb / bbl )
Rheological Properties
PHPA
0.35 lb/bbl
PHPA
0.52 lb/bbl
τy k n R2
τy k n R2
lbf /100 ft2 lbf-sn/100 ft2 lbf /100 ft2 lbf-sn/100 ft2
0.00 6.92 1.03 0.72 1.00 5.09 0.69 0.63 1.00
0.20 7.63 0.93 0.74 1.00 5.35 0.79 0.61 1.00
0.40 7.61 0.96 0.73 1.00 5.32 0.83 0.61 1.00
0.00 7.21 0.88 0.69 1.00 4.15 0.52 0.62 0.99
0.20 7.84 0.86 0.70 1.00 3.97 0.51 0.62 0.99
0.40 7.86 0.85 0.70 1.00 3.96 0.50 0.63 1.00
Rheological Properties
72°F 170°FComposition
FluidFiber Conc.
( lb / bbl )
OBM
(12.2 ppg)
SBM
(12.1 ppg)
48 | P a g e
4.6 Conclusions
This study was conducted to investigate the effects of temperature and fiber concentration on the rheology
of fiber-containing sweeps. Rheology experiments were conducted using rotational viscometers to
measure the rheology of base fluids and fiber-containing fluids at ambient temperature and 170°F. The
shear viscosity profiles of fiber sweep fluids were compared using graphical and curve-fitting regression
analyses. Based on the experimental results and data analysis, the following conclusions were made:
• The addition of fiber up to 0.08 weight percent has a minor effect on the fluid’s shear viscosity
profile, whether at ambient temperature or 170°F. Some instances showed slight increases in
viscosity, while others showed a decrease with increasing fiber concentration.
• Increasing the temperature of the fluid decreased the non-Newtonian behavior of the fiber fluid
and decreased the viscosity throughout the shear rate range of 2 to 1000s-1.
• In most cases, as fiber concentration increased, the viscosity showed increasingly non-Newtonian
behavior: in the Yield Power Law model, n decreased while K and τy increased.
• Neither oil-based nor synthetic-based fluids exhibited any significant shear viscosity sensitivity to
fiber concentration at ambient temperature or at 170°F. It may be possible for oil-based or
synthetic-based mud sweeps to be utilized in the field with no increase in ECD.
Nomenclature
BHA = Bottomhole Assembly
BP = Bingham Plastic
ECD = Equivalent circulating density
ERD = Extended reach drilling
K = Consistency index (lbf-sn/100 ft2)
N = Flow behavior index
ppg = Pounds per gallon
PAC = Polyanionic Cellulose
PHPA = Partially Hydrolyzed Polyacrylamide
PL =Power Law
XG = Xanthan Gum
YPL =Yield Power Law
Greek Letters
τ = Shear stress (lbf/100 ft2)
τy = Yield stress (lbf/100 ft2)
49 | P a g e
γ = shear rate (s-1)
µ = Viscosity
References
Ahmed, R.M. and Takach, N.E. 2008. Fiber Sweeps for Hole Cleaning. Paper SPE 113746 presented at
the SPE/ICoTA Coiled Tubing and Well Intervention Conference and Exhibition, The Woodlands,
Texas, 1-2 April. DOI: 10.2118/113746-MS.
Alderman, N.J., Gavignet, A., Guillot, D. and Maitland, G.C. 1998. High-Temperature, High-Pressure
Rheology of Water-Based Muds. Paper SPE 18035 presented at the SPE Annual Technical
Conference and Exhibition, Houston, Texas, October 2-5. DOI: 10.2118/18035-MS.
Bivins, C.H., Boney, C., Fredd, C., Lassek, J. Sullivan, P., Engels, J., Fielder, E.O. et al. 2005. New
Fibers for Hydraulic Fracturing. Schlumberger Oilfield Review 17 (2): 34-43.
Bulgachev, R.V. and Pouget, P. 2006. New Experience in Monofilament Fiber Tandem Sweeps Hole
Cleaning Performance on Kharyaga Oilfield, Timan-Pechora Region of Russia. Paper SPE 101961
presented at the SPE Russian Oil and Gas Technical Conference and Exhibition, Moscow, Russia, 3-6
October. DOI: 10.2118/101961-MS.
Cameron C. 2001. Drilling Fluids Design and Management for Extended Reach Drilling. Paper SPE
72290 presented at the IADC/SPE Middle East Drilling Technology conference, Bahrain, 22-24
October. DOI: 10.2118/72290-MS.
Cameron, C., Helmy, H., and Haikal, M. 2003. Fibrous LCM Sweeps Enhance Hole Cleaning and ROP
on Extended Reach Well in Abu Dhabi. Paper SPE 81419 presented at the SPE 13th Middle East Oil
Show and Conference, Bahrain, 5-8 April. DOI: 10.2118/81419-MS.
Demirdal, B., Miska, S., Takach, N.E. and Cunha, J.C. 2007. Drilling Fluids Rheological and Volumetric
Characterization Under Downhole Conditions. Paper SPE 108111 presented at the SPE Latin
American and Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, 15-18 April.
DOI: 10.2118/108111-MS.
Drilling Fluid Rheology. 2001. Kelco Oil Field Group, Houston, Texas (Rev. Sep 2005).
Gupta, V.K., Sureshkumar, R., Khomami, B. and Azaiez, J. 2002. Centrifugal Instability of Semidilute
non-Brownian Fiber Suspensions. Physics of Fluids 14 (6): 1958-1971
Hemphill, T. and Rojas, J.C. 2002. Drilling Fluid Sweeps: Their Evaluation, Timing, and Applications.
Paper SPE 77448 presented at the SPE Annual Technical Conference and Exhibition, San Antonio,
Texas, 29 September-2 October. DOI: 10.2118/77448-MS.
Maehs, J., Renne, S., Logan, B. and Diaz, N. 2010. Proven Methods and Techniques to Reduce Torque
and Drag in the Pre-Planning and Drilling Execution of Oil and Gas Wells. Paper SPE 128329
50 | P a g e
presented at the IADC/SPE Drilling Conference and Exhibition, New Orleans, Louisiana, 2-4
February. DOI: 10.2118/128329-MS.
Power, D.J., Hight, C., Weisinger, D. and Rimer, C. 2000. Drilling Practices and Sweep Selection for
Efficient Hole Cleaning in Deviated Wellbores. Paper SPE 62794 presented at the IADC/SPE Asia
Pacific Drilling Technology conference, Kuala Lumpur, Malaysia, 11-13 September. DOI:
10.2118/62794-MS.
Ravi, K.M. and Sutton, D.L. 1990. New Rheological Correlation for Cement Slurries as a Function of
Temperature. Paper SPE 20449 presented at the SPE Annual Technical Conference and Exhibition,
New Orleans, Louisiana, 23-26 September. DOI: 10.2118/20449-MS.
Robertson, N., Hancock, S., and Mota, L. 2005. Effective Torque Management of Wytch Farm
Extended-Reach Sidetrack Wells. Paper SPE 95430 presented at the SPE Annual Technical
Conference and Exhibition, Dallas, Texas, 9-12 October. DOI: 10.2118/95430-MS.
Swerin, A. 1997. Rheological properties of cellulosic fibre suspensions flocculated by cationic
polyacrylamides. Colloids and Surfaces A: Physiochemical and Engineering Aspects 133 (3): 279-
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Valluri, S.G., Miska, S.Z., Ahmed, R.M. and Takach, N.E. 2006. Experimental Study of Effective Hole
Cleaning Using “Sweeps” in Horizontal Wellbores. Paper SPE 101220 presented at the SPE Annual
Technical Conference and Exhibition, San Antonio, Texas, 24-27 September. DOI: 10.2118/101220-
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International Journal of Multiphase Flow 31 (2005) 318–336.
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Under Simulated Downhole Conditions. Paper SPE 109840 presented at the SPE Annual Technical
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51 | P a g e
5. Settling Behavior of Particles in Fiber-containing Drilling Fluids
Fiber-containing fluids are utilized in many industrial applications. In the upstream petroleum industry,
fiber suspensions are used to transport rock cuttings from the bottom of the hole to the surface. Moreover,
fibrous fluids are applied in fracturing operations to transport proppant particle to the fractured space.
Solids transport performances of these fluids largely depends on the settling behavior of suspended
particles.
This section of the report presents results of experimental and theoretical investigations conducted on the
settling behavior of spherical particles in fiber-containing fluid. Settling experiments were carried out in a
4-inch fully transparent cylinder that is sufficiently long (6.5 feet) to establish terminal settling conditions.
Both Newtonian and non-Newtonian fluids were considered in the investigation. A moving digital camera
system was used to track and locate a particle while it was settling in fully transparent test fluid. The
camera records were used to determine the settling velocity of each particle as a function of time. Tests
were performed with particles that have different sizes (2 mm to 8 mm). Fiber concentration was varied
from 0.00 to 0.08 percent by weight.
When a particle settles in the fibrous fluid, it experiences fiber drag in addition to the conventional
hydrodynamic resistance (i.e., viscous drag). Measured terminal velocity was used to compute the
viscous component of the total drag. Subsequently, applying the momentum balance, the fiber drag
component acting on the particle was determined from the total drag. Results showed that the fiber drag
was a function of the projection area of the particle, settling velocity, fiber drag coefficient, and density
difference between the fluid and particle. The fiber drag coefficient varied with Reynolds Number, fiber
concentration, and fluid behavior index. Using the experimental data, a semi-empirical model was
developed to predict terminal settling velocity of a particle in fiber-containing fluids. The correlation was
validated for both Newtonian and non-Newtonian base fluids that have low concentrations of hole-
cleaning fibers. The correlation is applicable to suspensions containing fully dispersed fibers with length
of approximately 10 mm and diameter of 100 µm.
5.1 Introduction
Settling and sedimentation occur in many areas of the petroleum industry and process engineering
operations. Typical applications of settling velocity include drill cuttings and proppants, transport
prediction, design of separators and settling tanks, and hydraulic and pneumatic transportation of solids
particle in mining, coal, and other industrial applications.
52 | P a g e
Studies on settling velocity of solids particles in Newtonian and non-Newtonian fluids have been well-
documented (Shah 1982; Klessidis 2004; Chhabbra & Peri 1991; Dallon 1967; Prakash 1983; Lali et al.
1989; and Chhabra 1980). Shah (1982) developed a new approach to analyze proppant settling in non-
Newtonian fluid. The study showed that the drag coefficient correlation is a function of Reynolds Number
and fluid behavior index ”n”. Especially at low Reynolds numbers, the fluid behavior index “n” has a
significant effect on the proppant settling velocity and this effect diminishes at high Reynolds Numbers. It
also shows that the correlation developed for static settling velocity can predict the dynamic settling data.
It was recommended to plot C���� versus Reynolds Number to get a better curve fit with a single straight
line on a log-log plot. The method had been tested (Shah et al. 2007) with data from the previous studies
(Dallon 1967; Prakash 1983; Lali et al. 1989; and Chhabra 1980) and satisfactory agreements had been
obtained. An experimental study (Fang 1992) conducted on free settling of spherical particles in
Newtonian and non-Newtonian fluids showed both stable and swinging settling patterns.
Particles in fluids with yield stress show different settling behavior. Fine and/or light particles can fully
suspend in the fluid due the yield stress. Dedegil (1987) developed a method to predict settling velocity
of particles in Herschel-Bulkley (Yield Power Law) fluid. The method relates the drag coefficient to the
generalized Reynolds Number based on apparent viscosity calculated from the representative shear rate
(V/d). The method accounts for the effect of yield stress on the settling velocity. It condensed most of the
published data (Valentik and Whitmore 1965) into a single curve when the drag coefficient was plotted
against the generalized Reynolds Number.
Many of the fluids used in the industry exhibit viscoelastic behavior. A study (Acharga 1986) conducted
on particle settling in viscoelastic fluid indicated that the fluid elasticity does not affect the settling rate in
the creeping flow region (low Reynolds Number). However, it enhances the sedimentation rate in the
transition zone. Predictions from a theoretical model were compared with measurements and showed
good agreement. Drag coefficient is strongly influenced by viscoelastic properties of the fluid.
Experiments (Jin and Penny 1995) revealed the variation of drag coefficient with the Reynolds Number
(NRep) and dimensionless viscoelastic parameter of the test fluid. In addition to fluid properties, the shape
of a particle has substantial effect on its settling behavior. Empirical models (Peden and Luo 1987; Chien
1994) developed to predict settling velocities of non-spherical particles showed the relationship between
the drag coefficient and shape factor.
Furthermore, the presence of a wall can create hydrodynamic interference with the settling particles. As
particles settle in fluids, their motion is affected by the presence of other particles and/or container walls.
The wall effect tends to reduce the settling velocity. The hydrodynamic effects of container walls have
53 | P a g e
been investigated (Brown et al. 1950; Lali et al. 1988; Di Felice et al. 1995) extensively. Experiments
(Lali et al. 1988 and Brown et al. 1950) showed that the diameter ratio (i.e., the ratio of the diameter of
the container to the diameter of the particle) and Reynolds Number determines the wall effect. Empirical
correlations are available to determine correction factors that account for the presence of a wall. These
factors relate the wall-free settling velocity to the actual velocity under both laminar and turbulent
conditions.
The presence of neighboring particles creates hydrodynamic interference that hinders particle
sedimentation. A number of experimental and theoretical studies (Richardson and Zaki 1954; Govier and
Aziz 1972; Smith 1997; Daneshy 1978) were conducted to investigate sedimentation in concentrated
suspensions, which demonstrated the reduction of settling velocity at high solids concentrations.
Increasing the particle concentration tends to increase the hydrodynamic interference and particle
collision, which are highly dependent on the flow regime (Govier and Aziz 1972). Uniformly-sized
particles in laminar motion have identical velocities, and collision is not expected even as concentration
increases. However, in turbulent flow collisions can occur due to settling speed differences that arise from
random fluctuations of fluid velocity. Moreover, in actual situations the solids particles do not have
uniform size distribution. As a result, even under laminar conditions, particle collision can exist. The
collisions intensify with the increase in particle concentration and differences in particle settling speeds.
Smith (1998) developed a theoretical model to predict the sedimentation velocity of uniformly-sized
particles in Newtonian fluid under laminar conditions. The model was compared with the correlation of
Richardson and Zaki (1954). Even though general agreement was obtained at high concentrations,
discrepancies were observed at low concentrations.
Rheological behavior of fiber suspensions is very complex. The introduction of fiber can significantly
alter the fluid rheology. Rajabian et al. (2008) developed a rheological model for fiber-containing
polymer suspensions. The model includes the fiber-fiber and fiber-polymer interaction. The experimental
measurements obtained from simple shear flows agreed with the model predictions. Another study of
fiber suspensions (Marti et al. 2005) showed minor gains in viscosity as the fiber concentration was
incrementally increased from an initial dilute suspension. However, at higher fiber concentrations, the
viscosity showed greater sensitivity to fiber concentration.
In the drilling industry, sweep fluid is used to improve wellbore cleaning in inclined and horizontal wells
when the regular drilling fluid fails to clean the wellbore sufficiently. Conventional sweeps are commonly
categorized as i.) high-viscosity; ii.) high-density; iii.) low-viscosity; iv.) combination; and v.) tandem
sweeps (Hemphill 2002). Sweeps provide a number of benefits, such as reducing cuttings beds and
54 | P a g e
subsequent decrease in annular pressure loss, as well as a reduction in torque and drag at the surface. As
a result, it is often applied to reduce excessive annular pressure losses and clean the wellbore prior to
tripping operation. Hole cleaning fiber is added to the sweep fluid to improve its performance with a
negligible increase in viscosity and pressure loss. Previous studies (Ahmed and Takach 2008; Cameron
et al. 2003; Bulgachev & Pouget 2006) reported that adding a small amount of hole cleaning fiber (less
than 0.1 percent by weight) improves solid transport performance of the sweep with no noticeable change
in fluid rheology.
Fiber has also shown considerable promise in well stimulation operations. Hydraulic fracturing requires
extremely high downhole fluid pressure to induce cracks into the reservoir rock, fracturing the formation.
A material that can withstand highly compressive forces, proppant, is necessary to prevent the fractures
from closing after the fluid pressure subsides and hydrocarbon production begins. As the fracturing fluid
is pumped downhole, the proppant travels with and behind it, and remains in the fracture after the fluid is
imbibed into the formation and/or flows back. With insufficient particle suspension properties, the
fracturing fluid will allow the proppant to settle before the fracture face closes and reduce the uniformity
and effectiveness of the proppant within the fracture. Conventional fracturing fluids rely on viscosity for
particle suspension, which precipitate excessive pressure losses and consequently require high pump
pressures. Fiber has been added to stimulation fluids to achieve the suspension properties necessary to
transport and deposit the proppant as designed, ensuring desired fracture conductivity and overall
productivity of the well. The fiber fluid can achieve equivalent suspension characteristics with less
viscosity, therefore requiring less pressure during stimulation operations. An experimental investigation
was conducted to evaluate the benefits of using fiber to prevent proppant settling in hydraulic fractures
(Bivins et al. 2005). Results showed a substantial reduction in the proppant settling velocity, which was
attributed to fiber concentration.
The settling behavior of particles in fiber suspensions is more complex than in the base fluid (i.e., fluid
without suspension). The interactions among the fiber particles, suspended solids and base fluid are
difficult, if not impossible, to express mathematically. When the fiber is fully dispersed in fluid, it can
form a stable network structure. The strength of the network depends on the fiber concentration and
length. Suspensions with low fiber concentrations and/or short fiber length form a very weak network.
The network structure created by the fiber particles tends to reduce the settling velocity of dense particles
due to fiber-fiber and fiber-particle interactions. The origins of these interactions can be mechanical
contact and/or hydrodynamic interference between fiber particles. Mechanical contact between fiber
particles generate a strong friction force that hinders the settling of suspended particles or drill cuttings. A
numerical investigation was conducted to study the settling of a small sphere through a suspension of
55 | P a g e
neutrally buoyant fibers (Harlen et al. 1999). The model considered fiber-fiber contact forces and long-
range hydrodynamic interactions. An asymptotic solution was presented for the limit when the sphere
diameter is much smaller than the fiber length and inter-fiber spacing. A greater understanding of particle
settling behavior in fiber suspension is essential to develop effective fiber-containing sweep and
fracturing fluid formulations.
5.2 Settling in Fiber Suspensions
Studies on the settling behavior of particles in both Newtonian and non-Newtonian fluid have been well
documented. Theoretical models have been established to predict terminal velocity of a particle. When a
particle settles in a homogeneous fluid, it experiences several forces. The major forces acting on the
particle when it attains its maximum speed (terminal velocity) are gravity, buoyancy, and hydrodynamic
drag. Considering these forces, the momentum balance for a settling particle is:
m �� F� � F� � F�� ………………..............……………………..……………………... (5.1)
where Fg and Fb are the gravity and buoyancy forces, respectively. The hydrodynamic drag (viscous drag)
force is expressed as:
F�� ��C��V�ρ�A� …………………...………..………….…………………………….... (5.2)
The above equation does not include the effect of fiber particles. After inserting the expressions for
gravity (Fg = mg), buoyancy (Fb = mgρf/ρp), and drag forces into Eqn. (5.1), we obtain the following
expression for the particle acceleration:
�� g ������� � �� �!"����# ..….………....………..…...…………..……………………… (5.3)
where m is mass of the particle; CDv is the viscous drag coefficient; and Ap is the projected area of the
particle in the plane perpendicular to the direction of flow. Under steady state (i.e., terminal settling)
condition, �� 0. Thus, the above equation reduces to:
g ������� � �� �%!"����# 0 ……………… ………………….………………………….…… (5.4)
When fiber is added to the fluid, an additional drag force (i.e., fiber drag) that opposes the particle motion
will be created because of mechanical and hydrodynamic interactions between the fiber and the settling
56 | P a g e
particle. In this case, the total drag force (FDT) acting on the particle is the sum of the viscous and fiber
drags. Applying momentum balance for steady state condition (dv/dt = 0), the total drag is:
F�& F' � F� …………………………………………………………….…………..…… (5.5)
Subsequently, the fiber drag can be determined from the total drag and viscous drag as:
F�� F�& � F�� ………………………………………………………………………….. (5.6)
It is important to note that both total drag and viscous drag must be determined at identical settling
conditions (i.e., at the same settling speed).
Despite the difference in origins between the fiber and viscous drags, similarities do exist. In less
concentrated fiber suspensions with short fiber particles, the major components of the two forces originate
from hydrodynamic effects. Considering this commonality, the fiber drag is modeled in a similar manner
as the viscous drag, resulting in:
F�� ��C��V(�)ρ� � ρ�*A� …………………………………………..…………………… (5.7)
whereC�� is fiber drag coefficient. The major dissimilarity between the fiber drag and viscous drag
equations is the use of density difference present in Eqn. (5.7), as compared to the singular fluid density
term in Eqn. (5.2). This formulation is based on experimental observations and provides the best
correlation with respect to the experimental measurements. Combining Eqns. (5.5), (5.6), and (5.7),
particle-settling velocity in fiber-containing fluid is:
V(� +,�-���.�� / 0�0�10�23 ..…………………………………………………………….……. (5.8)
In the case of fluid without fiber, the fiber drag coefficient in Eqn (5.8) becomes zero (CDf = 0), and the
equation reduces to the Stokes’ law:
V(� 45 ��� 6������� 7 ……………………………………………………….…..…………. (5.9)
5.3 Experimental Study
This investigation aimed at studying the settling behavior of solids particles in fiber suspensions and
determining the contribution of fiber drag to the total drag force. To achieve these objectives, a baseline
was first created to compare subsequent results. Settling velocity tests were conducted using base-fluids
57 | P a g e
(i.e., fluids without fiber), and correlations were developed to determine the viscous drag coefficients.
Then, settling velocity experiments were repeated using the base fluids with differing fiber
concentrations. The recorded terminal settling velocities of the particles in fiber suspensions, in
conjunction with the base fluid correlations, were used to determine the Reynolds Number and
corresponding viscous drag coefficient. Subsequently, the fiber drag coefficient was determined applying
Eqn. (5.8).
5.3.1 Experimental Setup
Settling velocity experiments were
conducted using a vertical cylinder with
spherical particles, using both Newtonian
and non-Newtonian base fluids. The
settling velocity of each particle was
measured by tracking the position of the
particle as function of time. The
experimental setup (Fig. 5.1) used in this
study consisted of a 10-cm diameter and 2-
m long fully transparent cylinder (i.e.,
polycarbonate tube). The ratio of the
particle diameter to the cylinder diameter
was maintained very low to reduce the
wall effect. The test section was
sufficiently long to ensure the
establishment of steady state (terminal
velocity) condition. A fully transparent
ruler was attached to the cylinder to
monitor the position of the particle while
settling. A moving digital video camera tracked the settling particle. The camera captured videos that
showed the exact position of the particles as a function of time. Back lighting was used to enhance the
clarity of the videos. At the bottom the settling cylinder, a manual valve was installed to discharge test
fluid when the experiment was completed. Experiments with non-Newtonian fluids were performed at
ambient temperature conditions. Tests with mineral oil were carried out at different temperatures to
increase the number of data points. Cooling water was circulated through a copper coil immersed in the
cylinder to maintain a constant fluid temperature condition during the experiment.
Fig. 5.1 Schematic of the experimental setup
Mixing Tank
Test Cylinder
Digital camera
Computer
Collator Tank
Cooling Water Inlet
Cooling Water Outlet
Fiber Water & Polymer
Settling P article
58 | P a g e
5.3.2 Test Materials
Experiments were performed using three different base fluids: i) Mineral oil (Newtonian fluid); ii) 0.5
percent polyanionic cellulose (Polypac R) solution; and 0.25 percent xanthan gum (Xanvis) solution.
Monofilament synthetic fiber particles (i.e., specific gravity of 0.9) were added to the base fluids to create
suspensions of differing fiber concentrations (0.00, 0.02, 0.04, and 0.08 percent by weight). The fiber
particles were flexible and easy to disperse in the fluid and had a relatively large aspect ratio (length = 10
mm and diameter = 100 µm). Spherical glass beads (2 mm to 8 mm) were used to carry out the
experiments. To increase their visibility, all beads were painted red. In confirmation of the rheological
study conducted in Section 4, the addition of fiber resulted in a negligible increase in shear stress (Fig.
5.2).
5.3.3 Test Procedure
A reliable test procedure was developed to measure settling velocity of solids particles in fiber
suspensions. All the experiments were carried out using the same test procedure that consisted of the
following:
Step 1. Fluid Preparation: Each experiment began by preparing the test fluid with desirable fiber and
polymer concentrations. First powder polymer and water were mixed in a 5-gallon container. The
polymeric fluid was left overnight to
hydrate. The required amount of fiber
was then added to the fluid and
agitated using a stand mixer to
achieve uniform dispersion. The
rheology of the fiber suspension was
measured using a rotational
viscometer (Fann 35).
Step 2. Cylinder Filling: The test fluid (base
fluid or fiber suspension) was then
transferred to the settling cylinder.
The back-light bulb was turned on
before dropping the particle into the
settling container.
Step 3. Particle Settling: The glass particles were soaked in a separate container of test fluid. Then,
each particle was brought to the center of the cylinder and released to settle in the fluid.
Step 4. Particle Tracking: As the particle settled through the fluid, it was tracked with the digital camera
Fig. 5.2 Rheologies of 0.5% PAC based fluids with different fiber concentrations
0
1
10
100
1 10 100 1000
Sh
ea
r S
tre
ss (
lbf/
ft^
2)
Shear rate (1/s)
0.00%
0.02%
0.04%
59 | P a g e
to record its position as a function of time.
5.3.4 Test Results
Using recorded video clips, the position of the
particle and corresponding time were
determined over the length of the settling
cylinder. The instantaneous settling velocity was
determined from the position of the particle and
settling duration (i.e., V(t) = ∆s/∆t). Fig. 5.3
presents the instantaneous settling velocity
verses settling time. The figure shows both the
transition and steady state settling regimes. At
the experiment’s initiation, the particle
accelerated variably for a short time until a
steady-state settling condition was established.
The experimental measurements obtained from
the base fluids (mineral oil and polymeric
fluids) were analyzed and plotted on Fig. 5.4 as
the drag coefficient versus particle Reynolds
Number (Rep). Experiments with mineral oil
were performed at different temperatures to
cover a wide range of Reynolds Numbers (Rep).
For Rep less than 0.8, the data points from the
mineral oil experiments were highly correlated
with the theoretical line (CDv = 24/Rep), as was
the Xanthan gum (XG)-based fluid. The
viscoelastic properties of the polymer solutions tended to stabilize the flow and maintain the laminar flow
conditions at higher particle Reynolds Numbers (Rep > 1.0). XG- based fluids have been known to delay the
onset of turbulence in pipes and annular flows (Escudier et al. 2009). Other high Rep data points also match
published measurements (Dedegil 1987) obtained from non-Newtonian fluids. The strong correlation
between the theoretical line and the experimental data points indicated the accuracy of the measurements and
minimal wall effect.
Fig. 5.3 Settling velocity of 6-mm spherical glass bead
As a function of time in 0.7% PAC
Fig. 5.4 Drag coefficient vs. particle Reynolds Number
for base fluids
0
10
20
30
40
0 3 6 9 12
Se
ttli
ng
Ve
loci
ty (
mm
/s)
Time (s)
Instantaneous Velocity
Terminal Velocity
1
10
100
1000
10000
0.01 0.1 1 10
Rep
CD
Non-New.
0.35%XG
0.25%XG
CD=24/Re
Mineral Oil
60 | P a g e
After establishing confidence in the measurements, settling tests were carried out using six different
polymer base fluids (0.50 percent polyanionic cellulose (PAC), 0.70 percent PAC, 1.00 percent PAC,
0.15 percent XG, 0.25 percent XG, and 0.35 percent XG). Fig. 5.5 shows the terminal settling velocity of
particles versus particle size for different fiber concentrations in 0.50 percent PAC base fluid. The
increase in fiber concentration consistently reduced the settling velocity. The smallest particle (2 mm)
was fully suspended when the fiber concentration increased to 0.04 percent. At high fiber concentrations
(greater than 0.04 percent), large particles were able to settle; however, at significantly reduced velocity.
The high fiber concentration (0.08 percent) fluid was able to completely suspended 2-mm and 3-mm
particles. Experimental results obtained from 0.25 percent xanthan gum solution (Fig. 5.6) showed a
similar trend in reduction of settling velocity. Particles less than 5 mm were fully suspended when the
fiber concentration was increased to 0.08 percent. In the XG-based fluids, the level of settling velocity
reduction is highly pronounced at low concentrations. As the concentration increased, the impact of fiber
diminished.
Fig. 5.5 Settling velocity particle in 0.5% PAC based fluid
for different fiber concentrations
Fig. 5.6 Settling velocity particle in 0.25% XG based fluid
for different fiber concentrations
No base fluids were able to suspend the particles fully. The base fluids tested did not exhibit high yield
stress and therefore could not support the particles under static conditions. As shown previously, fiber
has a minimal effect on fluid rheology. However, the fiber creates an additional drag mechanisms that can
resist the motion of the particle. The additional drag due to the fiber can originate in different ways.
Hydrodynamic effect of the fiber is critical at high settling velocities. As the settling velocity deceases,
hydrodynamic resistance diminishes. The mechanical drag resulting from fiber network could be another
mechanism that influences the behavior of particles. At low settling velocities, the mechanical drag
becomes the dominant force. As a result, the fiber network provides the resistance required to suspend
solids particles fully.
0
40
80
120
160
200
0 1 2 3 4 5 6 7
Te
rmin
al s
ett
lin
g V
elo
cit
y (
mm
/se
c)
Particle Size (mm)
0.00% fiber
0.02% fiber
0.04% fiber
0.06% fiber
0.08% fiber
0
40
80
120
160
200
0 1 2 3 4 5 6 7 8
Te
rmin
al s
ett
lin
g V
elo
cit
y (
mm
/se
c)
Particle Size (mm)
0.00% fiber
0.02% fiber
0.04% fiber
0.06% fiber
0.08% fiber
61 | P a g e
Figure 5.7 presents both the viscous and fiber drag forces as a function of fiber concentration. According
to Eqn. (5.5), at steady state conditions the total drag force balances the difference between the weight
and the buoyancy force. As a result, total drag remains constant as the fiber concentration increases. This
is because the addition of fiber does not have significant effect on the density of the suspension, which
affects the buoyancy force. In base fluid, the drag force develops only due to the viscous forces.
However, as the fiber concentration increases, the fiber drag becomes substantial resulting in reduced
settling velocity and viscous drag.
For a 5-mm particle (Fig. 5.7a), at approximately 0.04 percent the viscous and fiber drag forces became
comparable and the force curves cross each other. Field experiences show that fiber sweeps containing
nearly 0.04 percent provides optimum hole-cleaning with a limited quantity of fiber (Unnecessarily large
quantity of fiber in the mud circulation system can cause operational problems such as plugging of
downhole tools and surface separation equipment.). As the particle size decreased (Fig. 5.7b), the cross
point shifted toward the left, indicating the reduction in the fiber requirement in the sweep fluids. As
depicted from the figures, further increase in fiber concentration made the fiber drag asymptotically
approach the value of the total drag force. Therefore, the effect of fiber diminished as the concentration
increased.
(a)
(b)
Fig. 5.7 Comparison of fiber drag with viscous drag acting on a particle in 0.5% PAC based fluid as a function of fiber
concentration: a) 5-mm diameter particle; and 3-mm diameter particle
0.0
0.4
0.8
1.2
0.00 0.02 0.04 0.06 0.08
Dra
g F
orc
e (
mN
)
Fiber Concentration (%)
FDT
FDv
FDf0.00
0.05
0.10
0.15
0.20
0.25
0.00 0.02 0.04 0.06 0.08
Dra
g F
orc
e (
mN
)
Fiber Concentration (%)
Ftotal
FDv
FDf
62 | P a g e
5.4 Analysis of Results and Discussions
To develop generalized correlations for fiber drag coefficient, the experimental measurements (terminal
velocities) were used to determine the viscous drag coefficient (CDv) and particle Reynolds Number (Rep):
Re� ��%:;�� …………...………………………………………………………...……..…. (5.10)
where the apparent viscosity can be expressed as:
μ=�� τ? @ kBγ� D��� …...………………………………...……………………………… (5.11)
The representative shear rate �� EF/H. The viscous drag coefficient is calculated from Eqn. (5.2) using
the settling velocity data from the base fluid. Then, the fiber drag coefficient is determined from Eqn.
(5.8).
Figure 5.8 shows the fiber drag coefficient as a function of particle Reynolds Number for different fiber
concentrations. The data points formed a straight line on logarithmic plot with only minor deviations. In
order to get a single curve, the fiber drag coefficient was normalized by the fiber concentration as IJK/IL. After normalization, the data points from different fluids (both Newtonian and non-Newtonian
fluids) laid approximately on a single straight line on log-log plot (Fig. 5.9).
Fig. 5.8 Fiber drag coefficient vs. Reynolds Number for
0.7% PAC based fluid
Fig. 5.9 Normalized fiber drag coefficient vs. Reynolds
Number for different fluids
By applying regression analysis, the following correlation was developed to estimate the fiber drag
coefficient in Newtonian and Power Law fluids:
1
10
100
1000
0.01 0.1 1 10
Rep
CD
f
0.02%
0.04%
0.06%
10000
100000
1000000
10000000
0.01 0.1 1 10
Rep
CD
f/C
αα αα
n = 1.0
n = 0.8
n = 0.7
63 | P a g e
����M 4.47 Q 10SRe���.�TU ……………..…………………………..………………………. (5.12)
where the concentration exponent is:
V 1.4187 � 0.2397exp /�0.5 6ln 6 �`.aU�T7 /0.17637�2 …………………………...... (5.13)
5.5 Model Predictions
In order to assess the accuracy of Eqn. (5.12), model predictions were compared to experimental
measurements (Figs. 5.10 and 5.11). The comparison of results showed a good agreement between
measurements and predictions. This correlation demonstrated that fiber drag coefficient was a function of
particle Reynolds Number, fiber concentration, and fluid behavior index. A similar correlation was
developed to predict fiber drag coefficient in XG-based fluids, which exhibit yield stress. Results showed
a satisfactory agreement between measurement and predictions.
Fig. 5.10 Predicted vs. measured settling velocity for
different PAC based fluids
Fig. 5.11 Predicted and measured settling velocity vs. fiber
concentration for 0.5% PAC
1
10
100
1000
1 10 100 1000
Vs measured (mm/s)
Vs p
red
icte
d (m
m/s
)
Perfc line
n = 1.0
n = 0.8
n = 0.7
0
40
80
120
160
200
240
0.00 0.02 0.04 0.06 0.08
Teri
min
al sett
lin
g v
elo
cit
y (
mm
/sec)
Fiber concentration (%)
2 mm 3 mm
4 mm 5 mm
6 mm 2 mm
3 mm 4 mm
5 mm 6 mm
64 | P a g e
Figs. 5.10 and 5.11 provide better understanding
of the level of settling velocity reduction due to
the presence of fiber particles in the fluid system.
Addition of fiber had a more pronounced effect
on XG-based fluids than PAC-based fluids.
When 0.02 percent of fiber was added into the
XG-based fluid, a 50 percent or greater reduction
in the settling velocity was observed. However,
PAC-based fluids did not exhibit such a sharp
reduction. This could be attributed to the
difference in molecular structure. XG polymer
has a branched structure that tends to entangle with fiber particles to create strong polymer-fiber network,
which provides greater support to the particles.
5.6 Conclusions
Settling behavior of spherical particles in fiber-containing fluids was investigated. Fiber concentration
was varied 0.00 to 0.08 percent. Measurements showed significant reduction in settling velocity in fiber-
containing fluids. Based on the experimental results and theoretical analysis, the following conclusions
were made:
• Fiber particles that were uniformly dispersed in fluids hinder the motion and reduce the settling
velocity of suspended particles.
• Fiber concentration (up to 0.08 percent w/w) had a negligible effect on the rheological properties
of the fluid.
• The fiber drag or the hinder effect of the fiber was related to the fiber concentration, properties of
the fluid, and size, density, and settling velocity of the particle.
• Particles suspended in fiber sweep exhibited an additional drag force under both static and
dynamic conditions. The correlations developed in this investigation provided reasonable settling
velocity prediction in fiber suspensions.
Fig. 5.12 Predicted and measured settling velocity vs. fiber
concentration for 0.25% XG
0
80
160
240
320
400
480
0.00 0.02 0.04 0.06 0.08
Term
inal sett
lin
g v
elo
cit
y (
mm
/sec)
Fiber concentration (%)
2 mm 3 mm
4 mm 5 mm
6 mm 7 mm
2 mm 3 mm
4 mm 5 mm
6 mm 7 mm
65 | P a g e
Nomenclature
AP = projection area of a particle
CDv = Viscous drag coefficient
CDf = Fiber drag coefficient
d = diameter of a particle
FB = Buoyancy force
FD = Drag force
FDf = Fiber drag force
FDT = Total drag force
FDv = Viscous drag force
Fg = Gravitational force
g = gravitational acceleration
K = consistency index
m = Mass of a solids particle
NRep = Reynolds Number
n = fluid behavior index
Re = Reynolds Number
ReP = Particle Reynolds Number
t = Time
V = Instantaneous settling velocity of a particle
Vs = Terminal settling velocity of a particle
Greek Letters �� = Shear rate
µ = fluid viscosity
µapp = Apparent fluid viscosity
ρf = Fluid density
ρp = Density of a particle
τy = yield stress
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6. Hole-cleaning Performance of Fiber Sweeps
An experimental study was performed to investigate the rheology, hydraulics, and wellbore cleaning
(sweep tests) performance of aqueous and non-aqueous based fiber-containing fluids. The overall focus of
this entire body of research was to determine wellbore cleaning effectiveness of fiber-containing fluid
under actual field conditions. Despite the desire to simulate an operational scale environment, the
atmospheric conditions and functional variables were limited by the test equipment. As such, the system
was open to the atmosphere (standard atmospheric condition) and the operating fluid temperature could
be slightly elevated above ambient, as the water-based and synthetic-based fluids flowed through the
recirculation pump installed on the flow loop. In order to calibrate the equipment and perfect the
experimental procedures, some initial rheology and hole-cleaning experiments were run with water-based
xanthan gum fluid. The WBM sweep experiments were also used to correlate the critical cuttings velocity
model with experimental predictions (Section 7).
6.1 Introduction
Multiple field-tested techniques have been introduced over the years to prevent and reduce the proclivity
of drilled cuttings to settle within the wellbore, therefore improving hole-cleaning and cuttings transport.
Previous studies indicated that cuttings transport in directional wells is dependent on fluid rheology,
wellbore inclination angle, rotary speed of the drillpipe, flow rate, wellbore geometry, and other drilling
parameters (Valluri et al. 2006). Considering these factors, the easiest and most economical procedures
involve adding weighting agents and viscosifiers to the drilling fluid to increase the fluid's cutting
transport capability. As such, sweeps conventionally utilized in the industry are commonly categorized as
i) high-viscosity; ii) high-density; iii) low-viscosity; iv) combination; and v) tandem sweeps (Hemphill
2002). Sweeps provide a number of benefits, such as reducing cuttings beds and subsequent decrease in
annular pressure loss, as well as a reduction in torque and drag at the surface. Increasing the flow rate also
provides extra lifting potential of the sweeps but must be closely monitored depending on the
characteristics of the well. Pressure losses along the wellbore, as well as the equivalent circulating density
(ECD), must be considered when designing and applying sweep fluids. As a result, hole-cleaning fiber is
added to the sweep fluid to improve its performance with a negligible increase in viscosity and pressure
loss (George et al. 2011). Previous studies (Marti et al. 2005; Rajabian et al. 2005; Guo et al. 2005) also
showed similar trends, as the apparent viscosity of fiber-polymer suspensions slightly increased linearly
with increasing fiber concentration up to an approximate critical fiber concentration. At this critical
concentration, the apparent viscosity increased exponentially with a small increase in fiber concentration.
For field applications and for this study, fiber concentrations are relatively insignificant and well below
the critical threshold.
69 | P a g e
Previous experimental studies (Ahmed and Takach 2008) and field applications (Cameron et al. 2003;
Bulgachev & Pouget 2006) reported that adding a small amount of synthetic monofilament fiber (less
than 0.1 percent by weight) improves solid transport and hole-cleaning efficiency of the sweep over
comparable non-fiber sweeps, and with no noticeable change in fluid rheology. This favorable
performance may be attributed to the dynamic influence between the adjacent fibers. When fully
dispersed in the sweep fluid, fiber can form a stable network structure that tends to support cuttings due to
fiber-fiber and fiber-fluid interactions. The fiber-fiber interactions can be by direct mechanical contact
and/or hydrodynamic interference among fiber particles. Mechanical contact among fibers improves the
solids-carrying capacity of the fluid (Ahmed and Takach 2008). The mechanical contact between the
fibers and the cuttings beds aids in resuspending cuttings deposited on the low-side of the wellbore. As
the fibers flow through the annulus, mechanical stresses develop between the settled cuttings and the
fibers. These mechanical stresses result in a frictional force, which helps to re-suspend the cuttings, while
the fiber networks carry the solids to the surface. Also aiding in the solids transport is the fiber-fiber
interaction that enables the fiber network to move as a plug. Hence, at the surface of the cuttings bed the
fiber may have a higher velocity than the fluid phase, which is typically very low. These fast moving
fibers can therefore transfer more momentum to the deposited solids, overcoming the static frictional
forces and initiating particle movement.
6.2 Experimental Setup
Hole-cleaning abilities of fiber-containing fluids (fiber sweep), which are similar to those used for sweeps
in real wells, were investigated. Fiber sweep performance tests were conducted using a flow loop
apparatus (Fig. 6.1) available at the Well Construction Technology Center (WCTC). This device, as
currently configured (Fig. 6.2), provides the capability to perform pipe viscometer and annular hydraulic
measurements on any given fluid, as well as cuttings removal tests. The primary mechanical components
of the flow loop system are:
a. 150 gal mixing tank
b. Centrifugal pump
c. 4” x 2” annulus
d. 1.75” pipe viscometer
e. Two (2) hydrocyclones
f. Cuttings collection tank
g. Cuttings injection tank
h. Data Acquisition System (DAS)
70 | P a g e
The test fluid was mixed in the 150 gallon tank using a shaft and propeller agitator. The fluid then flowed
through the centrifugal pump, through 2-inch steel piping and the cuttings injection tank (when opened),
and into the two (2) parallel polycarbonate test sections. The two (2) test sections, 1.75-inch pipe
viscometer and 4 inch by 2 inch annulus, contained differential pressure (DP) meters which were
connected to a central desktop computer that contained the data acquisitions and control system (DAS).
All readings from the DP meters were recorded by the DAS. The DAS also controlled the flow rate and
drillpipe rotation and recorded all the system information, such as fluid temperature, pressure, density,
flow rate, and test time. Two coriolis flow meters (F1 and F2) were installed at the inlet and outlet of the
test sections. The flow meters measured mass flow rate and density of the fluid. The entire test section
was constructed as an independent unit that was connected to the pump and tanks by quick-connecting
hoses. The simply supported, hinged test section truss could be elevated at the free end to allow for an
inclined orientation.
The fluid from the test sections was then routed to a set of parallel hydrocyclones, which in turn routed
the cuttings to a collection tank below and returned the fluid to the mixing tank. During cuttings
collection, the valve between the collection and injection tanks was open. However, during cuttings
injection the valve was closed to prevent fluid backflow up through the hydrocyclones.
Fig. 6.1 Flow loop in inclined position
71 | P a g e
Fig. 6.2 Flow loop schematic
To simulate the cuttings that would be found in the
wellbore during drilling, 8/16-mesh silica sand was used.
The sand particles were circulated through the system and
used to create a bed in the annulus for wellbore cleaning
experiments. During the removal process, the sand was
diverted back to the collection tank through the
hydrocyclones. According to the sieve analysis (Fig. 6.3),
91 percent of the sand was 1.20 mm in diameter or greater
6.3 Experimental Procedure
Before wellbore cleaning experiments were run, the pipe
viscometer and annulus hydraulic measurements were
taken for the xanthan gum drilling fluid, unweighted SBM,
and the weighted SBM plus the incremental fiber concentrations. The process required from fluid
formulation to hole-cleaning efficiency results was as follows:
Fig. 6.3 Sieve analysis of silica sand, 8/16 mesh
(Test Methods: AASHTO T27, T11, T255, T248)
Fineness Modulus
No. 30
No. 8
3/8 inch
No. 4
No. 200 0.0
3.93
No. 50 0
No. 100 0
1
No. 16 9
96
100
100
SIEVE SIZE % PASSING
F1F1
∆P1
∆P2
F2
bypass pipe
Test section
Pump
Cutting Collection
or injection tank
Hydrocyclone
High speed
mixer
Mixing tank
V = 150 gal
Pressure transducer
Flow meter
∆P3
F1
Measuring tape
Computer
Bed height
Motor
Tank 1 Tank 2
Tank 3
Injection Tank
Injection Tank
V1
V2
V3
V4
72 | P a g e
Step 1. Preparation of Base Fluid: The fluids used for
the wellbore cleaning experiments were
unweighted xanthan gum drilling fluid (WBM)
and a weighted synthetic-based drilling fluid
system (SBM). This synthetic-based, invert
emulsion fluid system consisted of multiple
components (Fig. 6.4):
a) Synthetic-base (Internal Olefin, IO 16-18,
6.45 ppg)
b) Viscosifier
c) Lime
d) Primary and secondary emulsifiers
e) Brine
This fluid system shipped piecewise (Fig. 6.5), i.e., we were responsible for mixing the
components at the specified concentrations in order to achieve the proper invert emulsion
properties. Based on the required proportions in Fig. 6.6, the fluid was mixed using a high-speed
mixer (Fig. 6.7) and the following procedure:
a. Add base oil
b. Mix in lime and clay for 10 minutes
c. Add emulsifier(s) and mix for 10 minutes
d. Add brine and mix for 20 minutes
In order to utilize the available mixer, the fluid had to be mixed five (5) gallons at a time. Had a
larger mixer or dispersator been available, the mixing time would have been reduced
considerably. Each mixed five-gallon batch of synthetic-based fluid was then transferred to the
flow loop mixing tank (Tank 1).
Fig. 6.4 Synthetic-based fluid constituents
Viscosifier Lime CaCl2
Emulsifier – Primary
IO-16-18
Emulsifier – Secondary
73 | P a g e
Fig. 6.5 Packaged components of synthetic-based fluid
Fig. 6.6 SBM component concentrations Fig. 6.7 High-speed mixer
Syn B Base
Primary Emulsifier
Secondary Emulsifier
Lime Clay
Barite
CaCl2
74 | P a g e
Step 2. Weighting up (SBM): The WBM hydraulics and sweep experiments were conducted with
unweighted fluids (i.e., specific gravity of 1). By not introducing barite into the WBM, the
experimental error was reduced, and the cuttings behavior was easily observed in the annulus.
Adding barite would have resulted in a dark brown, murky colored fluid that would have
prohibited visual observation of cuttings beds removal.
Approximately 35 batches of unweighted SBM were mixed and transferred to the flow loop
mixing tank (Tank 1), with an estimated total weight of 955 lb. The unweighted SBM was
agitated in the mixing tank (Tank 1) to ensure homogeneity, and multiple samples were taken to
measure density, which equaled 7.43 lb/gal. For the wellbore cleaning experiments, the desired
fluid weight was 10.5 ppg. In order to achieve this fluid density, 675 lb. of barite were slowly
added to the mixing tank while the fluid was being agitated. In order to achieve maximum barite
dispersion and homogeneity, the fluid and barite were circulated through the flow loop, while also
being agitated in the mixing tank. After a sufficient length of time, multiple samples were again
taken from the mixing tank (Tank 1) and the density was checked. Taking the average of the
measurements, the density of the weighted fluid was calculated to be 10.6 lb/gal.
Step 3. Addition of Fiber: In a similar manner to the rheology and stability experiments, incremental
amounts of the synthetic monofilament fiber were added to the base fluid. A test matrix shows the
different variables and fiber concentrations used for the pipe viscometer and hole-cleaning
experiments (Tables 6.1 and 6.2). Based on the desired weight percentage, the quantity of fiber
needed for the experiment was determined and prepared.
The manufacturing and packaging process used for the fibers resulted in a compact mixture of
isotropic fiber clumps. When adding fiber to the sweep fluid on a rig, the fiber goes through the
hopper and exits the drillstring through the drill bit nozzle. The restriction at the bit results in
exponentially increased velocity, which immediately disperses the fiber. However, in the flow
loop, no such restriction existed, and the system pressure and maximum flow rate were incapable
of dispersion on their own. In order to promote a homogeneous fiber dispersion, the fiber clumps
were meticulously pulled apart before they were added to the system. The pulled fiber was added
to the mixing tank while the fluid was being circulated through the system. This was done to
enhance dispersion of the fiber and prevent the formation of clumps in the fluid.
75 | P a g e
Step 4. Pipe Viscometer Measurements: The test fluid (base fluid and fiber) was first thoroughly
homogenized by circulating through the flow loop at a high flow rate until the fluid temperature
reached approximately 40°C due to viscous heating. Once the fluid increased to proper
temperature, the flow was diverted through the 1.75-inch pipe viscometer. Starting with a flow
rate of 10 gpm, the fluid was allowed to flow until the data acquisition system stabilized the flow
rate and a sufficient number of data points were recorded. The flow rate was then adjusted
accordingly.
Step 5. Cuttings Bed/Accumulation in Annulus: Once all pipe viscometer measurements were taken,
the flow was diverted back to the annulus. The valve (V1) below the cuttings injection tank (Tank
2) was then opened, while the valve (V2) between the collection tank (Tank 3) and injection tank
(Tank 2) was closed. The flow was again initiated at a medium rate (∼ 40 gpm) until cuttings
begin to appear in the annulus. The flow rate was then decreased (∼ 10 gpm) to allow the cuttings
to settle out of the fluid and form a bed on the low side of the annulus. This process was
continued until the cuttings bed was sufficiently deep and is no longer increasing in depth. For the
high-inertia, SBM this process took up to 30 - 45 minutes, since the cuttings did not easily settle
out of the high yield stress, plug flow zone.
Step 6. Flush Cuttings from System: Once the cuttings bed was established, the injection tank (Tank 2)
outlet valve (V1) was closed, and the middle valve (V2) was opened. Then the valve to the
annulus (V3) was closed while the pipe viscometer valve (V4) was opened. Once the valve
configurations were complete, the fluid was pumped through the system at a high flow rate to
clear the piping of any remaining cuttings. This process was continued until no cuttings were
observed in the transparent pipe viscometer, and until the density readings of the inlet and outlet
coriolis flow meters (F1 and F2) were approximately equivalent.
Step 7. Sweep Fluid Circulation/Cuttings Removal: Once the latent cuttings were flushed from the
system, the flow was stopped and the annulus and pipe viscometer valves were opened and
closed, respectively. Flow again was initiated at a low flow rate (10 gpm), with or without pipe
rotation, depending on the test matrix. The fluid was circulated through the annulus until the
density readings the coriolis meters at the entrance and exit of the annulus converged to within
0.015 g/cc.
76 | P a g e
Step 8. Change in Inclination: The initial experiments were conducted with the annulus in the
horizontal position (θ = 90°). For each SBM and fiber formulation, the test matrix was followed
varying flow rate and pipe rotation in the horizontal orientation. Then, one end of the annulus test
section was elevated (θ = 72°) to simulate an inclined wellbore, as shown in Fig. 6.1. At this
annulus orientation, the test matrix experiments were ran again.
Modified Procedure in Step 6 for SBM Tests
Theoretically, after a certain amount of time at a steady flow rate, the fluid will have removed all
the cuttings possible at that given flow rate. That is, all possible cuttings from the top of the
cuttings bed will be swept away for a given fluid velocity and inertia. An increase in the flow rate
would result in an increase in velocity and accompanying inertia, which would remove another
layer of cuttings from the bed. However, with the weighted SBM, the density difference between
the annulus entrance and exit would never converge to 0.015 g/cc. This is attributed to the barite
in the fluid, which may result in some inconsistencies in density. One of the advantages of using
the non-aqueous fluid systems is their ability to suspend cuttings, and this may have attributed to
the non-converging densities. In other words, the fluid may have still been holding very fine sand
particles in suspension in the mixing tank and throughout the system.
Due to the difficulty in attaining a satisfactory density difference, the test procedure had to be
modified. In order to minimize error between the experiments, the sweep experiment time was
held constant at 30 minutes. The 30-minute duration was sufficient to establish equilibrium
conditions in the test section. The cuttings removal/sweep experiments were timed, the flow was
stopped after 30 minutes, and the data was recorded. This process was repeated for each flow rate
interval.
6.4 Experimental Test Matrix
Two hole-cleaning experiments (WBM and SBM) were conducted. The research was compartmentalized
to accommodate two diverging deliverables. The culmination of the first set of experiments allowed for
the subsequent modeling work and the initiation of the second set of experiments.
6.4.1 WBM Test Matrix
The first group of experiments focused on unweighted xanthan gum (FLO-VIS L) drilling fluid (WBM).
A test matrix of critical cuttings transport velocity experiments was developed to achieve the study
objectives presented in Section 7. The final matrix is shown in Table 6.1.
77 | P a g e
Sand particles with an average diameter of 2 mm were used in the experiment. The tests were performed
at different flow rates (20, 30 ... 100 gpm) to provide a wide range of bed height measurements. The
rheological properties of the test fluids were measured using rotational viscometers and presented in
Table 6.1. Two test fluids with similar flow curves were used in the sweep experiments.
Table 6.1 WBM flow loop test matrix and rheological properties
6.4.2 SBM Test Matrix
The second set of hole-cleaning experiments was conducted using weighted synthetic-based mud (SBM).
With respect to the original objectives of this project, these experiments were in accordance with the
project deliverables and provided insight into the performance of fiber-containing synthetic-based drilling
fluids. The test matrix for the SBM tests, shown in Table 6.2, contains the same variables.
Table 6.2 SBM flow loop test matrix
Fluid Fiber
concentration % by w/w
Drill pipe rotation (rpm)
Hole angle
Degree
Fluid properties
K (Pa.Sn)
n Ty
(Pa)
0.70% XG
0.00 0,25,50,75 90º, 70º 0.9 0.32 1.58
0.02 0,25,50,75 90º, 70º 0.9 0.32 1.58
0.04 0,25,50,75 90º, 70º 0.9 0.32 1.58
0.06 0,25,50,75 90º, 70º 0.9 0.32 1.58
Fiber Flow Rate
Concentration Q
( % ) ( gpm )
None
8.33 ppg
15.7 lb Flovis ® None
175 gal Water 8.33 ppg
None
7.50 ppg
Sweep Fluid
Synthetic-based
Fluid
XG-based Fluid
Synth
etic-b
ased
Mud (SB
M)
72°
72°
10 ‒ 80
10 ‒ 80
10 ‒ 80
10 ‒ 80
Weighting
Agent
Inclination
Angle
90°, 72°
Sweep
Experiment
Pipe
Viscometer
Y
Y
0.00
0.02
0.00
0.00
Y
Y
N
Y
Y
Y
90°, 72°
Barite
10.6 ppg
Barite
10.6 ppg
Barite
10.6 ppg
Barite
10.6 ppgSynth
etic-b
ased
Mud (SB
M)
10 ‒ 80
10 ‒ 80
10 ‒ 80
10 ‒ 80
90°, 72°
90°, 72°
90°, 72°
90°, 72°
0.06 Y
Y
Y
Y
Y
0.00
0.02
0.04
Y
Y
Y
78 | P a g e
6.5 Experimental Results
Using the previously described experimental setup and procedure, multiple tests were conducted and data
recorded. After Step 5 of the experimental procedure, the height of the cuttings bed was recorded at all 15
locations along the annulus. The measurement locations were demarcated by measuring tapes that have
been attached to the outside circumference of the annulus (Fig. 6.8). The average of these measurements
was calculated and recorded as the initial bed height. From the circumferential bed height measurements,
the fluid flow area could be calculated, as well as the cuttings bed wetted perimeter, hydraulic radius and
depth (Appendix D). Fig. 6.9 shows the average dimensionless bed height versus varying flow rates.
Fig. 6.8 Annulus test section bed height measuring tapes
Fig. 6.9 Bed height vs. flow rate for XG based fluid sweep (no fiber), inclined annulus (8.33 ppg)
6.5.1 Dynamic Variation of Cuttings Bed Height
The purpose of the annular test section in the flow loop was to provide a visual basis for measurements
and an understanding of flow behavior. In order to achieve the required visibility, the outer pipe must be
transparent, which requires relatively low strength pipe compared to the traditional casing or drillpipe.
Inlet Outlet
Measuring tape1 ft
15 ftSand height
Test section
0.00
0.20
0.40
0.60
0.80
0 20 40 60 80 100
Dim
en
sio
nle
ss
Bed
He
igh
t (h
/D)
Flow Rate, Q (gpm)
0 RPM
25 RPM
50 RPM
75 RPM
Polycarbonate was used for this outer pipe, and due to its susceptibility to cracking, a hollow, thin
pipe was used to simulate the drillstring. As such, the drillpipe
a completely centered eccentric position within the annulus. This
pipe rotation because the pipe wobble
annulus, hitting the sides of the outer polycarbonate tube.
After the cuttings bed built in the annulus, the drillpipe
therefore eliminating the possibility of visually confirming its eccentric location. In order to eliminate
error and provide repeatable results, the drillpipe
measurements are taken. During the prosecution of the sweep experiments when utilizing pipe rotation,
the cuttings bed height was observed to vary in rhythm wit
side of the cuttings bed rose while the other side dipped (
phenomenon was reversed.
Fig. 6.10 Fluctuation of cuttings bed height due to drillpipe
After the sweep experiment concluded, the drillpipe was manually rotated to the previously determine set
position. Once the drillpipe was static and in the correct position, the bed height measurements were
recorded. By repeating the same process for subsequent data collection, the possible error associated with
the varying bed height was eliminated.
6.5.2 Effect of Fluid Types
The emphasis of this study was on synthetic
on its ability to clean the wellbore. Due to the high cost of the SBM, only one test batch was created and
used for the sweep experiments. In order to perfect the experimental procedure, and for use as a
comparison to previous studies, a XG
The XG fluid was used to run the sweep experiments following the same experimental procedure and data
Polycarbonate was used for this outer pipe, and due to its susceptibility to cracking, a hollow, thin
pipe was used to simulate the drillstring. As such, the drillpipe was not overly heavily, and
a completely centered eccentric position within the annulus. This became particularly apparent during
wobbled in a random, unpredictable fashion down the entire length of the
of the outer polycarbonate tube.
After the cuttings bed built in the annulus, the drillpipe was completely covered by the sand particles,
therefore eliminating the possibility of visually confirming its eccentric location. In order to eliminate
provide repeatable results, the drillpipe was manually rotated to the same position every time
measurements are taken. During the prosecution of the sweep experiments when utilizing pipe rotation,
the cuttings bed height was observed to vary in rhythm with the drillpipe rotation. As the pipe rotated, one
side of the cuttings bed rose while the other side dipped (Fig. 6.10). As the pipe continued to rotate, this
Fig. 6.10 Fluctuation of cuttings bed height due to drillpipe rotation
After the sweep experiment concluded, the drillpipe was manually rotated to the previously determine set
position. Once the drillpipe was static and in the correct position, the bed height measurements were
process for subsequent data collection, the possible error associated with
the varying bed height was eliminated.
on synthetic-base mud (SBM) and the effect of introducing synthetic fiber
bility to clean the wellbore. Due to the high cost of the SBM, only one test batch was created and
used for the sweep experiments. In order to perfect the experimental procedure, and for use as a
comparison to previous studies, a XG-based, unweighted, polymeric fluid was mixed in the flow loop.
The XG fluid was used to run the sweep experiments following the same experimental procedure and data
79 | P a g e
Polycarbonate was used for this outer pipe, and due to its susceptibility to cracking, a hollow, thin-walled
ly, and did not rest in
particularly apparent during
fashion down the entire length of the
completely covered by the sand particles,
therefore eliminating the possibility of visually confirming its eccentric location. In order to eliminate
manually rotated to the same position every time
measurements are taken. During the prosecution of the sweep experiments when utilizing pipe rotation,
h the drillpipe rotation. As the pipe rotated, one
). As the pipe continued to rotate, this
After the sweep experiment concluded, the drillpipe was manually rotated to the previously determine set
position. Once the drillpipe was static and in the correct position, the bed height measurements were
process for subsequent data collection, the possible error associated with
base mud (SBM) and the effect of introducing synthetic fiber
bility to clean the wellbore. Due to the high cost of the SBM, only one test batch was created and
used for the sweep experiments. In order to perfect the experimental procedure, and for use as a
meric fluid was mixed in the flow loop.
The XG fluid was used to run the sweep experiments following the same experimental procedure and data
80 | P a g e
gathering processes. For the sake of time, the entire text matrix was not completed, stopping after the
addition of 0.02 percent w/w of fiber.
The WBM and SBM sweep experiments
initiated with the base fluid (no fiber). The
cuttings removal efficiency was plotted as a
function of flow rate (Figs. 6.11 and 6.12).
Despite the limited amount of data gathered for
the polymeric fluid sweep experiments, a trend
emerged that could be extrapolated to compare
to other fluid sweep tests.
When comparing the WBM and the SBM fluids,
the density and rheology of the two fluids must
be taken into consideration. Weighted fluid
provides a significantly increased inertial force
over unweighted fluids. This alone can provide
an increased cuttings carrying capacity and
improved hole-cleaning. To make a fair
comparison, the SBM sweep data should be
handicapped to eliminate the density benefit.
Even so, prediction will still favor the SBM,
since the fluid system shows an unequivocal
advantage in cuttings suspension and flow. It
should also be noted in Fig. 6.11 that the lines
diverge at high flow rates. In essence, the SBM
provides an overall cleaner wellbore at the
experiment culmination, despite similar trends
between the two fluids at lower flow rates.
Another visible difference between the two fluids was physical and macroscopic appearances. The XG-
based fluid was lightly colored, and the cuttings particles were easily identified within the fluid. This
enabled very accurate bed height measurements. This contrasts with the experiences from the SBM sweep
experiments. The base, unweighted synthetic-base drilling fluid (7.6 ppg) was slightly off-white in color
Fig. 6.11 Bed height vs. flow rate for WBM and SBM, no
rotation, inclined annulus
Fig. 6.12 Percent reduction of bed height of WBM and SBM,
no rotation, inclined annulus
0.00
0.20
0.40
0.60
0.80
0 20 40 60 80
Dim
en
sio
nle
ss
Be
d H
eig
ht
(h/D
)Flow Rate, Q (gpm)
SBM (10.6 ppg)
XG (8.33 ppg)
0
20
40
60
80
100
20 30 40 50 60 70 80
% B
ed
Heig
ht
Re
du
cti
on
Flow Rate, Q (gpm)
WBM (8.33 ppg) SBM (10.6 ppg)
81 | P a g e
and clean. Once barite was added to the system, the color changed to dark brown, and small barite clumps
could be seen floating in the fluid. This provided difficulty in precisely measuring the bed height because
the dark color of the fluid closely matched that of the cuttings particles. Therefore, bed height
measurements were taken based on the shaded areas of the annulus, present from the cuttings beds inside.
Individual cuttings particles could no longer be identified. Due to the density of the fluid and the particles
suspended within, the coriolis flow meters were constantly measuring relatively large differences in
density. The difference was apparent during rheology and hydraulics measurements, but it was
exacerbated during sweep experiments. The ability of the fluid to suspend the cuttings and the presence of
the barite clumps, provided for a constantly changing fluid density.
The greatest advantage evident from the experimental results was the greater ability of the SBM over the
XG-based fluid to reduce the cuttings beds with a reduced pressure loss. Using strictly water-based muds,
an increase in viscosity or density would be required to increase cuttings removal, but it would
detrimentally result in increased pressure loss in the annulus and pipe. However, the weighted SBM is
able to eliminate cuttings beds and the accompanying measured apparent viscosity is less than that
measured for the unweighted WBM (Fig. 6.13).
Fig. 6.13 Apparent viscosity vs. shear rate for sweep base fluids, 95°F
10
100
1,000
10,000
1 10 100 1,000
Ap
pa
ren
t V
isc
os
ity
(cp
)
Shear Rate (s-1)
XGM (8.33 ppg)
SBM (10.6 ppg)
SBM (7.5 ppg)
82 | P a g e
6.5.3 Effect of Fiber Concentration
In accordance with the test matrix, four (4) fluid formulations were tested; base fluid, 0.02, 0.04, and 0.06
percent by volume. In theory, with each incremental increase in fiber concentration, the wellbore cleaning
effect should improve. In essence, more fiber equates to less cuttings beds. This hypothesis is based partly
on conventional wisdom and partly on previous experimental studies. Previous works have shown that
adding small amounts of fiber to the sweep fluid can improve cuttings removal (Ahmed and Takach
2008). This phenomenon may hold true unless the fiber concentration is great enough to influence the
rheology of the suspending fluid drastically, at which point the advantages of fiber are no longer relevant.
The test matrix for this experimental phase of the work only includes fiber concentrations proven to
provide little to no rheological influence.
The fiber was added to the system after each
successive round of experiments, and in
accordance with the experimental setup and
procedure. As stated previously, two (2) test
batches of XG-based fluid (WBM) were mixed
to test the experimental procedure and provide a
comparison to the ensuing SBM tests. As shown
in Fig. 6.14, adding a small amount of fiber
(0.07 lb/bbl) to the fluid resulted in an overall
increase in cuttings bed removal. This advantage
is particularly noticeable at high flow rate. At
the maximum flow rate of 80 gpm, the bed
height after the fiber sweep was almost 50
percent of the bed height after the base fluid
sweep.
It should also be noted that only the fiber fluid
could completely clean the wellbore during the
sweep experiment (Fig. 6.15). While this
required some pipe rotation, the fiber provided
obvious benefits, since the base fluid alone
could not completely clean the wellbore unless
high pipe rotation speeds (75 rpm and 60 gpm)
Fig. 6.14 Bed height vs. flow rate for WBM, no rotation,
inclined annulus
Fig. 6.15 Comparison of fiber effectiveness for hole-cleaning
with WBM (8.33 ppg), inclined annulus
0.20
0.40
0.60
0.80
0 20 40 60 80 100
Dim
en
sio
nle
ss
Be
d H
eig
ht
(h/D
)
Flow Rate, Q (gpm)
Base Fluid
0.02% Fiber
0
20
40
60
80
100
30 50 70
% B
ed
He
igh
t R
ed
uc
tio
n
Flow Rate, Q (gpm)
No Fiber - 0 rpm
0.02% Fiber - 0 rpm
No Fiber - 50 rpm
0.02% Fiber - 50 rpm
83 | P a g e
were applied.
Introducing fiber into the weighted synthetic-based fluid (SBM) provided slightly different results. Due to
the weight of the fluid, the inertial force of the moving fluid in the annulus was greater than that of the
unweighted XG-based fluid. This factor alone could have provided enhanced hole-cleaning performance
over the WBM. The inertia of the SBM could have limited the significance of the addition of the fiber. As
shown in Figs. 6.16 to 6.18, the addition of fiber in the horizontal and inclined annulus, without pipe
rotation, provided no real predictable or reliable benefit to cuttings bed eradication. This was in contrast
with the results from the WBM sweep experiments, in which the addition of a small amount of fiber
resulted in a decrease in bed height over the base fluid (Fig. 6.14).
When the annulus was in the horizontal position, the inertial force pushing the cuttings through the
annulus was at the maximum. This left little room for improvement with the addition of fiber. However,
in the inclined position, the cuttings wanted to slide down the annulus, creating more work for the sweep
fluid. Critical evaluation of Fig. 6.18 showed that in the inclined position, the high concentration fiber
sweep provided visual and measurable improved wellbore cleaning over the base fluid. This trend was
slightly apparent at low flow rates, but it became unequivocally obvious at high flow rates. The addition
of fiber may have increased the lifting capacity of the sweep fluid, which enabled the fluid to carry the
cuttings through the annulus and return them to the collection/accumulation tank.
(a)
(b)
Fig. 6.16 Dimensionless bed height vs. flow rate for SBM, no pipe rotation
a) Horizontal annulus, and b) Inclined annulus
0.00
0.20
0.40
0.60
0.80
0 20 40 60 80
Dim
en
sio
nle
ss B
ed
He
igh
t (h
/D)
Flow Rate, Q (gpm)
Base Fluid
0.02% Fiber
0.04% Fiber
0.06% Fiber
0.00
0.20
0.40
0.60
0.80
0 20 40 60 80
Dim
en
sio
nle
ss B
ed
He
igh
t (h
/D)
Flow Rate, Q (gpm)
Base Fluid
0.02% Fiber
0.04% Fiber
0.06% Fiber
84 | P a g e
Fig. 6.17 Dimensionless bed height vs. flow rate for WBM, no pipe rotation, horizontal annulus
(a)
(b)
Fig. 6.18 Percent bed height reduction vs. fiber concentration for SBM, no pipe rotation
a) Horizontal annulus, and b) Inclined annulus
With pipe rotation, the benefits of fiber became more apparent. Sweep experiments conducted without
pipe rotation left residual cuttings in the annulus after 80 gpm (Fig. 6.19). Compare this with tests
conducted at 25 rpm pipe rotation, as the wellbore is completely cleaned with a flow rate of 40 gpm (Fig.
6.20). As stated previously, the benefits were negligible in the horizontal position. However, adding fiber
to sweep fluids in the inclined annular position provided marked improvement in wellbore cleaning.
0.00
0.20
0.40
0.60
0.80
1.00
0 20 40 60 80 100
Dim
en
sio
nle
ss b
ed
heig
ht
(h/D
)
Flow rate (gpm)
0.0 rpm (0.00% fiber)
0.0 rpm (0.02% fiber)
0.0 rpm (0.04% fiber)
0
20
40
60
80
100
0 0.02 0.04 0.06
% B
ed
Heig
ht
Red
ucti
on
% Fiber Concentration
80 gpm
60 gpm
40 gpm
20 gpm
0
20
40
60
80
100
0 0.02 0.04 0.06
% B
ed
Heig
ht
Red
ucti
on
% Fiber Concentration
85 | P a g e
(a)
(b)
Fig. 6.19 Percent bed height reduction vs. flow rate for SBM, no pipe rotation
a) Horizontal annulus, and b) Inclined annulus
(a)
(b)
Fig. 6.20 Percent bed height reduction vs. flow rate for SBM, 25 rpm pipe rotation
a) Horizontal annulus, and b) Inclined annulus
6.5.4 Effect of Inclination Angle
In accordance with the test matrix, the sweep experiments were conducted in horizontal (90°) and
inclined (72°) annular orientations. The 72° inclination angle represents the approximate maximum safe
height the end of the annulus test section could be raised. This required reconfiguring of the support
braces and the rerouting and stabilization of the fluid return lines.
Inclination angle played an important role in visualizing the effectiveness of the fiber sweeps. As stated
previously, the fiber sweeps provided no real significant improvement over the base sweeps in the
horizontal annular position. The wellbore cleaning effectiveness of the base weighted synthetic-based
fluid was so great that the addition of any hole-cleaning aid would be inconsequential. However, in the
0
20
40
60
80
100
20 50 80
% B
ed
He
igh
t R
ed
ucti
on
Flow Rate, Q (gpm)
0
20
40
60
80
100
20 50 80
% B
ed
Heig
ht
Re
du
cti
on
Flow Rate, Q (gpm)
100
No Fiber 0.02% Fiber 0.04% Fiber 0.06% Fiber
0
20
40
60
80
100
10 20 30
% B
ed
Heig
ht
Re
du
cti
on
Flow Rate, Q (gpm)
0
20
40
60
80
100
10 20 30
% B
ed
Heig
ht
Re
du
cti
on
Flow Rate, Q (gpm)
100
No Fiber 0.02% Fiber 0.04% Fiber 0.06% Fiber
86 | P a g e
inclined annular position, the addition of fiber provided observable decreases in bed height (Fig. 6.21). At
most flow rates, adding fiber to the sweep fluid provided an approximate two-fold decrease in bed height
over the base sweep fluid.
(a)
(b)
Fig. 6.21 Percent bed height reduction vs. inclination angle for SBM
a) 20 gpm, and b) 40 gpm
Fig. 6.22 presents equilibrium bed high
measurements obtained under horizontal and
inclined configurations with WBM. In
general, the inclination effect on the bed
height was moderate. Without pipe rotation,
an inclined wellbore was slightly easier to
clean than horizontal. However at high flow
rates (above 80 gpm), this trend changed.
The horizontal test section was completely
cleaned while some cuttings were still in the
inclined annulus at the same flow rate.
0
20
40
60
80
100
90 72
% B
ed
He
igh
t R
ed
ucti
on
Inclination Angle (deg)
0
20
40
60
80
100
90 72
% B
ed
He
igh
t R
ed
ucti
on
Inclination Angle (deg)
0.06% Fiber, 25 rpm0 Fiber, 25 rpm0.06% Fiber, 0 rpm0 Fiber, 0 rpm
Fig. 6.22 Dimensionless bed height vs. flow rate for WBM base
fluid, horizontal and inclined annulus
0.00
0.20
0.40
0.60
0.80
1.00
0 20 40 60 80 100
Dim
en
sio
nle
ss b
ed
heig
ht
(h/D
)
Flow rate (gpm)
0.00 rpm ( Hor.conf.)
50.0 rpm (Hor.Conf.)
0.00 rpm (Inc. Conf.)
50.0 rpm (Inc. Conf.)
87 | P a g e
6.5.5 Effect of Flow Rate
As mentioned previously, the maximum allowable flow rate is a critical component in designing sweeps
used in the field. The best cleaning results are typically obtained at maximum pump rate. However, the
maximum rate may cause an undesirable increase in the equivalent circulating density, which is limited
by the pore and fracture pressures.
Aside from fiber concentration, flow rate was the most critical variable in determining the effectiveness of
fiber sweeps on cuttings removal. Per the experimental procedure, the flow rate was varied from 10 gpm
to approximately 80 gpm, the system’s maximum attainable flow rate. Cuttings bed measurements were
taken after each 30-minute, static flow rate sweep experiment. As predicted, cuttings removal increased as
flow rate increased (Fig. 6.23). This trend persisted regardless of the inclination angle, pipe rotation, or
fiber concentration. However, a phenomena developed during some of the sweep experiments. As shown
in Figs. 6.9 and 6.23, a flat spot appeared in the cuttings removal/flow rate graphs. This plateau was
immediately followed by another positive-slope bed height reduction trend. This was thought to be
attributed to some critical cuttings transport velocity. Essentially, a small range of flow rates existed that
could no longer remove cuttings from the cuttings bed. Once the flow rate threshold was exceeded, the
sweep was able to remove cuttings again, reducing the bed height.
Fig. 6.23 Percent bed height reduction vs. flow rate for SBM base sweep (no fiber)
0
20
40
60
80
100
0 10 20 30 40 50 60 70 80
% B
ed
Heig
ht
Re
du
cti
on
Flow Rate, Q (gpm)
Horiz, 25 rpm
Incl, 25 rpm
Horiz, 0 rpm
Incl, 0 rpm
88 | P a g e
6.5.6 Effect of Pipe Rotation
In accordance with the test matrix, two rotational speeds were chosen to provide similarity with actual
field practices. The maximum revolutions per minute for the sweep experiments was held at 50. At 50
rpm, the cuttings removal efficiency was comparatively high. Increasing the rotational speed above 50
rpm provided no real significant increase in cuttings removal. In addition, the eccentricity of the drillpipe
resulted in rhythmic contact and vibration between the 2-inch drillpipe and the 4-inch polycarbonate tube
(casing). At 50 rpm, the vibrations caused by the wobbling drillpipe were severe, and increasing the
rotational speed would have increased the vibrations and possibly reduced the life expectancy or damaged
the flow loop apparatus.
For a given flow rate and fluid formulation,
the cuttings removal was significantly
improved when the drillpipe was rotated
(Figs. 6.24 and 6.25). The benefit of pipe
rotation was more noticeable in the inclined
annulus (Fig. 6.24b). Increasing the pipe
rotation speed from 25 to 50 rpm resulted in
a larger measured increase in cuttings
removal for a given fiber concentration over
that measured at similar test conditions in
the horizontal position. The rotation of the
pipe agitated the bed, lifted bed particles,
and facilitated the removal process of
cuttings. Regardless of the inclination, it provided substantial improvement in the hole-cleaning
performance of the fluid at low and intermediate flow rates.
Fig. 6.24 Effect of different pipe rotation speeds on the hole-
cleaning for WBM
0.00
0.20
0.40
0.60
0.80
1.00
0 20 40 60 80 100
Dim
ensi
on
less
bed
heig
ht
(h/D
)
Flow rate (gpm)
0.00 rpm (0.00% fiber)
25.0 rpm (0.00% fiber)
50.0 rpm (0.00% fiber)
75.0 rpm (0.00% fiber)
89 | P a g e
(a)
(b)
Fig. 6.25 Percent bed height reduction vs. fiber concentration for SBM, Q = 20 gpm
a) Horizontal annulus, and b) Inclined annulus
6.6 Pipe Viscometer Measurements
Measuring fluid rheology in a pipe viscometer provides a relatively greater knowledge of fluid behavior
under actual flow conditions. It also provides another metric of quantitatively identifying the influence of
different additives on the flow behavior of the base fluid. A number of pipe viscometer tests were
performed to: i) study the effect of fiber concentration on a critical Reynolds number for the transitional
from laminar to turbulent condition; ii) compare flow curves of base fluid and fiber sweeps; iii) evaluate
theoretical model prediction using experimental results; and iv) investigate drag reduction behavior of
fiber suspension. Base fluid and fiber sweep exhibit similar pressure loss behavior. However, fiber tends
to reduce the pressure loss slightly. The results are consistent with previously reported studies (Ahmed
0
20
40
60
80
100
0.00 0.02 0.04 0.06
% B
ed
Heig
ht
Red
ucti
on
% Fiber Concentration 0 RPM
25 RPM
50 RPM
0
20
40
60
80
100
0.00 0.02 0.04 0.06
% B
ed
Heig
ht
Red
ucti
on
% Fiber Concentration
90 | P a g e
and Takach 2008; Xu and Aidum 2005), which showed that small amounts of fiber have a negligible
effect on the pressure loss.
The pipe viscometer is one of the two parallel test sections (Fig. 6.2) and contains two differential
pressure (DP) meters (Fig. 6.26). The spacing between the two capillary lines for each DP meter is
different to serve as a redundant check for evaluating the flow data.
Pipe viscometer experiments were conducted to determine the flow behavior effect of introducing fiber
into the sweep fluid. Pipe viscometer rheology was recorded for every fluid+fiber formulation listed in
the test matrix (Tables 6.1 and 6.2).
Fig. 6.26 Pipe viscometer schematic
The DP meters functioned as transducers, converting the hydraulic differential pressure energy into an
electrical current, which was then sent to the Data Acquisition System (DAS). The DAS controlled the
flow rate of the centrifugal pump, and recorded flow rate, pressure drop, temperature, pressure, and
density. Therefore, the pipe viscometer experiments measured pressure loss as a function of flow rate
(Fig. 6.27). For the WBM, the base fluid and fiber sweeps showed similar pressure loss (Fig. 6.27a). The
addition of fiber even slightly reduced pressure loss at higher flow rate. This trend conflicted with that
observed with the SBM. The measured pressure loss as a function of flow rate showed that under low
flow rates (laminar conditions) the addition of fiber resulted in an increase in pressure loss (Fig. 6.27b).
DP 2
DP 3
12.188”
38.625”
Flow
20.00’
1.75”
91 | P a g e
(a)
(b)
Fig. 6.27 Measured pressure loss as a function of flow rate in pipe viscometer, 90° orientation:
a) WBM; and b) SBM
The measured pressure losses were converted to the Reynolds numbers and associated friction factors for
the varying flow rates (Fig. 6.28). For the WBM, the critical Reynolds number (Re) was approximately
2700. The fiber concentration had a minor effect on the critical Reynolds number. Under laminar
conditions, slight reduction in pressure loss or friction factor was observed. After evaluating the
dimensionless groups for the SBM, the flow was laminar at all flow rates, which was attributed to the
weight of the fluid because the density prevented the onset of turbulence given the flow rate and pipe
diameter.
(a)
(b)
Fig. 6.28 Fanning friction factor vs. generalized Reynolds number in pipe viscometer:
a) WBM; and b) SBM
0
0.1
0.2
0.3
0.4
0.5
0.6
0 20 40 60 80 100
∆P
(
ps
i )
Flow Rate, Q (gpm)
SBM-7.5 ppg
No Fiber
0.09 lb/bbl Fiber
0.18 lb/bbl Fiber
0.001
0.01
0.1
1
100 1000 10000
Fr
icti
on
fa
cto
r,
f
General Reynolds number
Predicted
0.00%fiber
0.02%fiber
0.04%fiber
0.06%fiber
16/Re
TurbulentLaminar
0.001
0.01
0.1
1
100 1000 10000
Fri
cti
on
fa
cto
r,
f
General Reynolds number, Re
Syn-base fluid (7.5 ppg)
SBM - No Fiber
SBM - 0.02% Fiber
SBM - 0.04% Fiber
16/Re
0
0.05
0.1
0.15
0.2
0.25
0 20 40 60 80 100
Pre
ssu
re l
oss
(p
si)
Flow rate (gpm)
0.00%fiber
0.02%fiber
0.04%fiber
92 | P a g e
6.7 Wellbore Hydraulics
In a similar manner to the pipe viscometer experiments, hydraulics studies were conducted with fluid
flowing through the annulus test section. The annulus test section sat parallel to the pipe viscometer, and a
differential pressure meter that was attached to the annulus with capillary lines approximately four feet
apart measured pressure drop as a function of flow rate (Fig. 6.29). Hydraulic measurements were taken
of every fluid+fiber formulation listed in the test matrix (Tables 6.1 and 6.2). The differential pressure
measurements were recorded and graphed (Fig. 6.30). However, the pressure measurements for the fiber
sweep fluids were in error, as the recorded data provided illogical results. It was speculated that this was
the result of fiber plugging of the capillary lines. Therefore, the SBM fiber sweep pressure data was left
off of Fig. 6.30.
(a)
(b)
Fig. 6.30 Measured pressure loss as a function of flow rate in annulus, 90° orientation:
a) WBM; and b) SBM
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 20 40 60
Pr
es
su
re
lo
ss
(p
si)
Flow rate (gpm)
0.00% fiber
0.02% fiber
0.04% fiber
0.06% fiber
0
0.01
0.02
0.03
0.04
0.05
10 20 30 40 50 60 70 80
Pres
su
re L
oss
(
ps
i / ft
)
Flow Rate, Q (gpm)
SBM - 10.6 ppg (Base)
SBM - 7.50 ppg (Base)
Fig. 6.29 Annulus test section schematic
DP 1
47.875”
Flow
22.00’
4.0
”
2.0
”
93 | P a g e
In Fig. 6.31, measurements are presented as Fanning friction factor versus Reynolds number for the
WBM. Per the figure, every test was carried out under laminar flow conditions. The pump rate and
annular dimensions did not promote turbulent flow.
Fig. 6.31 Fanning friction factor vs. generalized Reynolds number in annulus
6.8 Conclusions
An experimental study was conducted on the wellbore cleaning efficiency of fiber-containing water-based
and synthetic-based fluids. These fluids represent commonly used drilling fluids in the industry, and
satisfy the requirement of using fluids relevant to offshore, deepwater operations. The two fluids,
unweighted xanthan gum-based fluid and weighted synthetic-based mud, were each mixed with varying
fiber concentrations. A flow loop test apparatus was utilized to conduct the cleaning experiments, as well
as measure pressure drop in a pipe viscometer. By varying flow rate, inclination angle, fiber
concentration, and pipe rotation, a great amount of data were gathered that was used to evaluate the
optimum conditions to use these fiber sweeps. The following were concluded from the experiments:
• Very dilute concentrations of fiber in the XG based fluid had no significant influence in
measureable pressure loss compared to the fiber-free base fluid.
• Introducing fiber into synthetic-based fluid resulted in an increase in pressure loss at low flow
rates. However, this disparity disappeared as the flow rate increased, and the pressure loss versus
flow rate curves converged at high flow rates.
0.01
0.1
1
10
1 10 100 1000 10000
Fri
ctio
n f
act
or,
f
Reynolds number
PR0.00%fiber0.02%fiber0.04%fiber0.06%fiber16/Re
94 | P a g e
• For a non-rotating pipe case, noticeable increase in cuttings removal was not observed with
increasing fiber concentration. The inertia of the weighted fluid is great enough to mask any
slight improvement that might be gained by adding fiber to the system.
• With pipe rotation, cuttings removal increased with the introduction of fiber to the system. Only a
slight amount of fiber was necessary to observe the improved wellbore cleaning performance of
the fiber sweep over the base fluid sweep.
• Maximum wellbore cleaning performance with a very dilute concentration of fiber was achieved
at maximum flow rate and pipe rotation.
6.9 Guidelines
The applicability of this study to the industry is apparent in the experimental results. As this study was
oriented towards offshore, deepwater drilling operations, the results regarding oil-based muds and
synthetic-based muds are of the utmost importance. The rheological studies implicate that the addition of
fiber up to 0.08 percent will have no significant impact of rheology, and subsequently the hydraulics and
ECD will remain unaffected. The sweep experiments and pipe viscometer rheology also reinforce the
usefulness of fiber in sweep fluids. Under similar conditions, fiber sweeps improved wellbore cleaning
over base fluid sweeps. Taking this into consideration, the recommendations here-to-fore in the use of
fiber-containing sweeps are as follows:
• Utilize base sweep fluids that have gelling property (i.e., measurable yield stress). The presence
of yield stress is necessary to achieve stable and homogeneous suspension of fiber particles
within the sweep fluid.
• Use fiber concentration of approximately 0.04 percent. As shown in Section 5.3.4, the best hole-
cleaning performance is generally achieved with an optimum fiber concentration that makes the
fiber drag comparable with the viscous drag force. Increasing fiber concentration beyond this
optimum value results in minimal cleaning improvement. In addition, using optimum fiber
concentration will ensure a minimal ECD influence.
• Rotate the drillstring while applying fiber sweep material to optimize wellbore cleaning. Without
drillstring rotation, the performance improvement obtained from the application of fiber sweep is
minimal.
95 | P a g e
Nomenclature
bbl = Barrel
cp = Centipoise
DAS = Data acquisition system
DP = Differential pressure
ECD = Equivalent circulating density
gpm = Gallons per minute
K = consistency index
n = fluid behavior index
ppg = Pounds per gallon
Q = Flow rate
Re = Reynolds number
rpm = Rotations per minute
SBM = Synthetic-based mud
Ty = yield stress
WBM = Water-based mud
XG = Xanthan Gum
Greek Letters
θ = Inclination angle �� = Shear rate
µ = fluid viscosity
96 | P a g e
References
Ahmed, R.M. & Takach, N.E. 2008. Fiber Sweeps for Hole Cleaning. Paper SPE 113746 presented at the
SPE/ICoTA Coiled Tubing and Well Intervention Conference and Exhibition, The Woodlands,
Texas, 1-2 April.
Bulgachev, R.V. & Pouget, P. 2006. New Experience in Monofilament Fiber Tandem Sweeps Hole
Cleaning Performance on Kharyaga Oilfield, Timan-Pechora Region of Russia. Paper SPE
101961 presented at the SPE Russian Oil and Gas Technical Conference and Exhibition,
Moscow, Russia, 3-6 October.
Cameron, C., Helmy, H., & Haikal, M. 2003. Fibrous LCM Sweeps Enhance Hole Cleaning and ROP on
Extended Reach Well in Abu Dhabi. Paper SPE 81419 presented at the SPE 13th Middle East Oil
Show and Conference, Bahrain, 5-8 April.
George, M.L., Ahmed, R.M. & Growcock, F.B. 2011. Rheological Properties of Fiber-Containing
Drilling Sweeps at Ambient and High Temperature Conditions. Paper AADE-11-NTCE-35
presented at the AADE National Technical Conference & Exhibition, Houston, Texas, USA, 12-
14 April.
Guo, R., Azaiez, J., & Bellehumeur, C. 2005. Rheology of Fiber Filled Polymer Melts: Role of Fiber-
Fiber Interactions and Polymer-Fiber Coupling. Polymer Eng. and Sci. 45 (3): 385-399.
Hemphill, T. & Rojas, J.C. 2002. Drilling Fluid Sweeps: Their Evaluation, Timing, and Applications.
Paper SPE 77448 presented at the SPE Annual Technical Conference and Exhibition, San
Antonio, Texas, 29 September-2 October.
Marti, I., Hofler, O., Fischer, P. & Windhab, E.J. 2005. Rheology of Concentrated Suspensions
Containing Mixtures of Spheres and Fibres. Rheologica Acta 44 (5): 502–512
Rajabian, M., Dubois, C., & Grmela, M. 2005. Suspensions of Semiflexible Fibers in Polymeric Fluids:
Rheology and Thermodynamics. Rheologica Acta 44 (5): 521–535.
Valluri, S.G., Miska, S.Z., Ahmed, R.M. & Takach, N.E. 2006. Experimental Study of Effective Hole
Cleaning Using “Sweeps” in Horizontal Wellbores. Paper SPE 101220 presented at the SPE
Annual Technical Conference and Exhibition, San Antonio, Texas, 24-27 September.
97 | P a g e
7. Mechanistic Modeling of Hole Cleaning with Fiber Sweeps
The mechanistic model presented in this study is an extension of existing cuttings transport models
(Ahmed et al. 2002; Duan 2005; Larsen et al. 1997; Clark et al. 1994). It was developed to predict critical
transport velocity (CTV) in fiber-containing fluid. The CTV for fiber-containing fluid is different from
that of the fluid without fiber (base fluid). Adding fiber to the base fluid creates additional force, fiber
drag force, acting on bed particles in the same direction as the viscous drag force. The fiber drag can
initiate particle movement even at low fluid velocities in which the viscous drag is minimal. As shown in
Eqn. (5.7), the fiber drag is a function of the fiber drag coefficient, and a reliable correlation is needed to
estimate the coefficient. A mathematical model for the CTV has been developed considering linear and
angular momentum balances of a bed particle.
7.1 Introduction
Mathematical hole-cleaning models are often preferred because of their wide range of applicability. Clark
and Bickham (1994) presented a mechanistic model for predicting the minimum fluid velocity for
transporting cuttings without formation of a cuttings bed. This model considers major forces acting on a
single stationary cuttings particle deposited on the surface of the bed. To verify the model, they performed
flow loop tests using different test fluids (water, solution of HEC, and xanthan gum). The tests were run
at angles ranging from near vertical (20° minimum) to horizontal (90°). The model prediction showed a
good agreement with the experimental results. Recently, an improved mechanistic model (Ahmed et al.
2002) was developed to predict the critical transport velocity (CTV). The model was verified using
experimental data obtained using water and polypnoinic cellulose suspension as test fluids. The average
cuttings size was varied from 0.125 mm to 3.5 mm. The model predictions showed satisfactory agreement
with experimental measurements.
Although mechanistic models provide general CTV predictions for different drilling applications, their
accuracy is lower than that of the empirical models. To improve the accuracy of the mechanistic models,
studies were conducted to develop models that combine both mechanistic models and empirical
correlations. Rasi (1994) presented a semi-empirical model that combines fluid mechanics-based
analytical model with correlations developed using experimental and field data. Later, an improved semi-
empirical model (Larson et al. 1997) was developed to predict the required critical transport velocity in
high angle wells. The model was developed after performing an extensive experimental study using a
medium-scale flow loop. The model predicted critical transport velocity and annular cuttings
concentration under different drilling conditions for highly deviated and horizontal wells. The study
concluded that cuttings start to accumulate in the wellbore if the annular velocity becomes insufficient,
98 | P a g e
below the critical transport velocity. More recently, Ozbayoglu et al. (2007) developed a three-layer
cuttings transport model applying the principles of mass and momentum balance for steady, isothermal
flow condition. The model is valid for both compressible and incompressible drilling fluids.
Basic Assumptions
The following basic assumptions are made to develop the present model:
1. A flat and uniform layer of cuttings bed forms in the wellbore.
2. The variation in bed thickness along the length of the wellbore is negligible.
3. Cuttings particles are assumed spherical with uniform size and density.
4. Flow is steady and isothermal.
5. Solid concentration in the fluid layer above the bed is negligible.
6. Particle collision has a minor effect on the critical transport velocity.
Assuming uniform bed thickness greatly simplified the modeling, even though in some cases ripples and
dunes form in the wellbore. The formation of ripples and dunes complicate the flow geometry and make
the modeling extremely difficult. Ripples and dunes usually form when the flow velocity is close to the
critical transport velocity and bed particle size is comparable with the thickness of viscous sub-layer. By
using the average bed thickness, it was more convenient to define the critical transport velocity.
Another important simplifying assumption was that there were no suspended solids in the fluid. The
presence of suspended particles tends to create collision phenomena. In addition to hydrodynamic forces,
the collision helps to initiate the movement of bed particles. This phenomena is largely dependent on the
size of both suspended and bed particles. The effect of the collision is negligible when the suspended
particles are very small compared to bed particles.
7.2 Forces Involved in Particle Transport
Analyzing solids bed removal process and resuspension phenomena requires a good understanding of the
forces acting on a single bed particle. The momentum exchange between the bed particle, and the fluid
represents the external force that is imposed on the particle. As depicted on Fig. 7.1, a single particle
located on the cuttings bed surface is subjected to the three major forces: weight of the particle (gravity),
buoyancy force hydrodynamic drag and lift forces, and plastic force due to the gelling characteristics of
the fluid. The hydrodynamic drag and lift forces are created due to the fluid flow over bed particles. When
they become strong enough, these forces can initiate particle movement either in the form of rolling or
99 | P a g e
lifting of the particles. Net non-hydrodynamic torque is
the sum of torque generated by gravity, buoyancy, and
plasticity at point P. The net torque is independent of
fluid velocity. Particle rolling is initiated when the
moment generated by the hydrodynamic forces at point P
overcome the net torque. Similarly, the lifting occurs
when the y-component of the resultant force developed
by gravity, buoyancy, plasticity and hydrodynamic forces
becomes positive (upward).
7.2.1 Gravity and Buoyancy Forces
Gravity and buoyancy forces are major forces that act on
the bed particle under dynamic and static conditions. These forces act in opposite directions and have
contradictory effects on hole cleaning. Cuttings particles deposit on the borehole wall and form beds
because gravity dominates the buoyancy force. Buoyancy force is a function of density of the fluid and
hence weighted muds have the potential to provide effective hole cleaning. Nevertheless, due to ECD
limitation mud weight cannot be increased substantially for improving hole-cleaning. The buoyancy force
acting on a bed particle is expressed as:
F� cU d�5ρ�g (7.1)
And the weight of the particle is calculated as:
F� cU d�5ρ�g (7.2)
where ρ� and ρ� are particle and fluid density, respectively.
7.2.2 Hydrodynamic Forces
The hydrodynamic drag (FD) and lift force (FL) develop under dynamic conditions. These forces generate
when a body moves relative to its surrounding fluid. The hydrodynamic drag (viscous drag) acts in the
direction of the fluid upstream velocity. The lift force acts perpendicular to upstream velocity. These
forces develop as a result of pressure and stress variations on the surface of the particle due to the action
of the surrounding fluid. They can be determined by integrating the wall shear stress and pressure
distributions on the surface of the particle (Fig. 7.2):
F� ∮PcosθdA @ ∮τk(sinθdA (7.3)
Fig. 7.1 Forces acting on single bed particle
Ф
α
FL
FP
W
FD
P
U
FDf
Xy
100 | P a g e
Fm �∮PsinθdA @ ∮τk(cosθdA (7.4) where P is pressure normal to the small surface area,
dA, nopF is the wall shear stress tangent to the surface
area, and θw (or θ) is the angle between upstream
velocity and pressure direction.
The wall shear stress and pressure distributions are
required to determine the lift and drag forces using
Eqns. (7.3) and (7.4). However, it is difficult to
obtain these distributions experimentally or mathematically. Therefore, experimentally obtained drag and
lift coefficients are commonly utilized to determine these forces. The viscose drag force acting on the
flow protruding bed particle is:
F� ��C��ρ�u�A (7.5)
Similarly, the lift force is expressed as:
Fm ��Cmρ�u�A (7.6)
where u is the local velocity and A is the projected area of the particle above the mean bed surface where
the hydrodynamic forces are acting perpendicular to this area.
Drag Coefficient
Various analytical, numerical, and experimental investigations (Guogui 1992; Dedegil 1987) have been
conducted to estimate drag coefficient for both Newtonian and non-Newtonian fluids. A commonly used
correlation (White 1991) for a wide range of particle Reynolds number can be used to determine the drag
coefficient. The correlation is valid for both creeping and turbulent flow regimes.
C�� �4rs� @ U�.rs�t.u @ 0.4 (7.7)
The drag coefficient is a function of the bed particle properties such as shape, size, orientation, and
surface roughness, as well as fluid properties and flow parameters. This equation can be applied for
Newtonian and non-Newtonian fluids if the particle Reynolds number is defined in generalized form
(Dedegil 1987).
Fig. 7.2 Drag and lift force acting on the surface of a
bed particle
Drag force
Lift force
θw
pdA
�dis dA
N
u
101 | P a g e
Rv� w!��x (7.8)
The shear stress, τ, is evaluated at the representative shear rate of (u/dp). Eqn. (7.7) was developed and
used to predict drag coefficient of a single particle without considering the effect of neighboring particles.
In order to predict reasonable values of drag force, the equation should be modified to account for the
variation of drag coefficient due to the presence of other particles on the surface of the solids bed (Ahmed
et al. 2002). An extensive experimental study (Liang et al. 1995) performed to determine the effect
surrounding particles on drag coefficient presented a correction factor, Dr, which varies from 1.05 to 0.35.
The correction factor is 1.05 without the presence of particles and 0.35 with the presence of several
neighboring particles. Due to the presence of many particles on the surface of the bed, more realistic
value for the correction is 0.35. However, during model testing and calibration, the best drag correction
factor was found to be 0.4.
Lift Coefficient
Lift force exists due to the asymmetry in the flow field around the particle. The asymmetry flow condition
is established because of the no-slip boundary condition at the cuttings bed surface. This phenomenon is
responsible for the lift mechanism. A small spherical particle moving through very viscous liquid in slow
shear flow experiences a lift force resulting from the velocity gradient (Saffman 1964). Two assumptions
are made in the development of Saffman’s lift force equation: i) the particle is not influenced by solid
boundaries, and ii) constant fluid velocity gradient. The equation is expressed as:
Fm 1.615 4�!:y! 6w?7`.S (7.9)
where v is the kinematic viscosity and y is the vertical distance from the mean bed level. The validation of
his formula is limited to instances in which certain values of gradient Reynolds number, Rvz d�Bdu/dyD| , Rep and ReG is less than unity. By combining Eqns. (7.6) and (7.9), lift coefficient can be
expressed as:
Cm 4.11 - �wrs� w?3`.S (7.10)
7.2.3 Fiber Drag Force
When fiber is introduced to pure liquid, an additional drag force will develop if the particle slips in the
fluid or the fluid flows past the particle. Fiber drag force, F��, acts in the same direction as the viscous
drag force (Fig. 7.1). In order to estimate this force, a model has been developed. Even though limited
102 | P a g e
studies (Bivins et al. 2005; Harlen et al. 1999) have been conducted on the settling behavior of particle in
liquid, the settling mechanisms present in fiber-containing fluid have not been fully understood.
In this study, the contribution of fiber drag to the total drag force was experimentally investigated.
Empirical correlations that relate the fiber drag coefficient to the fiber concentration were developed. The
definition for the fiber drag force is presented in Section 5.2. The fiber drag coefficient for fluid without
yield stress is expressed as:
����M 4.47 Q 10SRev���.�TU (7.11)
where the concentration exponent is:
α 1.4187 � 0.2397exp /�0.5 6ln 6 �`.aU�T7 /0.17637�2 (7.12)
The concentration is a function of the fluid behavior index for Power Law fluids. Xanthan gum-based
fluids exhibit yield stress under ambient temperature. The drag coefficient for these fluids does not follow
the same trend. It is also affected by the yield stress in addition to the fluid behavior index. Hence, the
following drag coefficient correlation has been developed for these types of fluids.
����M 1335Rev��`.~U� (7.13)
The concentration exponent is calculated as:
α 3.2271n�� � 3.3965n� @ 1.441 (4.14) where k� τ? @ k , and
n� �� log /x�.�B�``D�x�.� 2 (7.15)
7.2.4 Plastic Force
Pore spaces are occupied by drilling fluid. The upper portion of the cuttings bed is exposed to the
dynamic of the liquid phase while the fluid in the interstitial can be stagnant (Fig. 7.3). The stagnant fluid
can form gel that tends to hold bed particles and prevent them from moving. The plastic force acting on a
single particle that is fully surrounded by stagnant fluid is estimated as F� 0.5πd��τ? , where n� is the
yield stress. Clark and Bickham (1984) introduced a method to estimate plastic force for bed particles that
are partially surrounded by stagnant fluid. The plastic force that holds a spherical bed particle is expressed
as:
103 | P a g e
F� 0.5πd��τ? �∅ @ 6c� � ∅7 sin�∅ � cos∅sin∅� (7.16)
where ∅is the angle of repose.
7.3 Near-Bed Velocity Profile
Forces that are developed under dynamic condition
such as hydrodynamic force and fiber drag are
affected by the local velocity close to the center of
the particle. Therefore, in order to predict these
forces, a model that describes the local velocity at the
bed particles is necessary.
7.3.1 Newtonian Fluid
The law of the wall is often used to describe the near-bed velocity profile under turbulent flow condition.
Person (1972) developed a general formula of the law of the wall for Newtonian fluid. This correlation is
valid for both the viscous sub-layer as well as the turbulent boundary layer.
y. �� @ ABe� � 1 � w� 0.5w� � 0.33w5 � 0.0417w4D (7.17)
where � �.�, A=0.1108, the Von karman constant, ko = 0.4, and dimensionless velocity �. ���. When the dimensionless bed particle size, H�. o���y , is greater than 70, the roughness of the bed largely
affects the velocity profile. As a result, the above formulation of the law of the wall will not be applicable
(Gerhart et al. 1992; White 1991).
7.3.2 Non-Newtonian Fluid
In order to apply the law of the wall for non-Newtonian fluids, the apparent viscosity can be used instead
of Newtonian viscosity. However, using the apparent viscosity concept to calculate velocity profile for
fluid with yield stress does not provide reliable velocity predictions. Desouky and Al-Saddique (1999)
developed a formula to predict local velocity profile of Yield Power Law fluid.
Velocity Profile in the Viscous Sub-layer
Most modern drilling fluids are expected to have a thick laminar sub-layer due to their high yield stress.
The velocity profile in the viscous sub-layer (y+ < δ+) defined as:
u. y. (7.18)
Fig. 7.3 Stagnant fluid surrounding a bed particle
(Ahmed et al. 2002)
Ø
Stagnant fluid region
Flow
104 | P a g e
where y. is the dimensionless distance from the mean bed surface and is expressed as
y. y�Ux��� 6���7, y is the distance from the mean bed surface, Ux 6x�s��� 7`.S , and n��o is average of
bed shear stress, n��o ���o ���!� . Dimensionless thickness of the laminar sub-layer, δ. is calculated as:
δ. δ�Ux��� 6���7 (7.19)
where
δ S����rs� 6 �K� ¡7`.S (7.20)
Substituting u+ and y+ into Eqn. (7.18) and rearranging it:
u y 6x�s�� B1 � xD7�/� (7.21)
Hence, the local velocity gradient can be determined from the above equation.
w? 6x�s�� B1 � xD7�/� (7.22)
X x�x�s� (7.23)
where n is the fluid behavior index, and K is the consistency index.
Velocity Profile outside the Viscous Sub-layer
Outside the viscous sub-layer, the velocity profile for Yield Power Law fluid is determined using the
following formula.
u £¤� ¥¦1 � �?�§@ ln¨1 � ¦1 � �?�§©ª @ U#=« (7.24)
where U#=« is the maximum fluid velocity that can be expressed as:
U#=« �6x�s�� B1 � xD7��/� δ � £¤�t �1 @ ln 6 ¬�§7� (7.25)
Similarly, the velocity gradient can be obtained from the above equation.
105 | P a g e
w? £¤�t ���§¦!���
@ ��§®¦��!����6��!���7¯° (7.26)
The annular flow Reynolds number can be expressed in a generalized form.
Rv�� a£!��x± (7.27)
where τ� is the wall shear stress. According to Ahmed and Miska (2009), the average wall shear stress in
a concentric annulus can be calculated using the narrow slot approximation technique.
��£�²��³ )x±�x�*6´µ�� 7
��́x±! 6 5��.��7 6τ� @ 6 ��.��7 τ?7 (7.28)
In order to calculate average bed shear stress,τ�v, the bed friction factor,���o , must first be obtained.
Many correlations (Dodge and Metzner 1959; Colebrook 1939) have been developed to estimate friction
factor for Newtonian and non-Newtonian fluids under turbulent flow conditions for both smooth and
rough pipes and annuli. Reed and Pilehvari (1993) proposed the following correlation for non-Newtonian
turbulent flow in rough pipe.
�·K �4log¨`.�T¸�s�� @ �.�U�1´.!)rs��KB´1�/!D*�1t.¹u© (7.29)
where ε is absolute pipe roughness, which is a function of the angle of repose, ∅; effective diameter, Dv��; andgeneral Reynolds number, Rv��, that can be obtained from Eqn. (7.27). According to Duan
(2005), pipe roughness, ε �� B1 @ sin∅D. The hydraulic diameter, Dhyd is used to approximate the
effective diameter.
D§? "�¾².¾³.¾� (7.30)
where Af is the flow area above the cuttings bed, So is the wetted perimeter of the wellbore, Si is the
wetted perimeter of the drill pipe wall, and Sb is the wetted perimeter of the cuttings bed. Calculation
procedure for the area and perimeter is shown in Appendix A. For the laminar regime, bed friction factor
reads:
���o �Urs�� (7.31)
106 | P a g e
7.4 Mechanistic Model Formulation
In order to determine the mechanical equilibrium status of a single bed particle, the net torque at the
contact point, P (Fig. 7.1), and the resultant left force in the lateral direction must be determined. Lifting
of the particle occurs when the inclination angle is low (nearly vertical). However, in horizontal and
highly deviated wells bed particles that are exposed to the fluid movement start rolling when the net
rotating torque has a positive value. Forces acting on a single particle are shown on Fig. 7.1. The contact
point P is considered as the axis of rotation during rolling. Particles rolling over the surface of the bed
have been visually observed during laboratory experiments at high inclination angles. Applying the
angular momentum balance at point P, the rotating torque, ΓÀ , can be expressed as:
ΓÁ �� ÂF�sinϕ @ F��sinϕ @ Fmcosϕ � F�cosϕ � )F� � F�*sinBα @ ϕDÄ (7.32a)
where α and ϕ are the inclination angle and angle of repose, respectively. By substituting the force
expressions developed in the Section 7.2 into Eqn. (7.32a), the following simplified equation for torque
can be obtained.
ΓÁ c�,��4 ����(k�∅.�Å�� (k�Æ.�ÇÈÉ(Æ4 u� � x�ÈÉ(∅��� � ��B(��D(k�BÊ.∅D5 � (7.32b)
where, s is the ratio of the density fluid to that of the solid and Dr is the drag correction factor. The
following steps show the numerical procedure:
1. A constant flow rate is set at a certain value.
2. Maximum and minimum bed height values are selected to determine the average bed height.
3. Hydraulic diameter and generalized Reynolds number are calculated.
4. Bed friction factor is obtained from Eqn. (7.29) or (7.31).
5. The local velocity and velocity gradient should be determined from Eqns. (7.21 to 7.26).
6. Reynolds number is calculated particle using Eqn. (7.27).
7. Drag and lift coefficients are estimated using Eqns. (7.7 to 7.15).
The forces acting on the particle are predicted using Vr. Eqn. (7.5) and (7.6) and substituted into
Eqn. (7.32a).
8. If ΓÁ > 0.0, then the maximum value of bed height is replaced by the average value. Otherwise,
the minimum value of bed height is replaced by the average value and the procedure requires
repeating Steps 2 to 8 until ΓÁ converges to a certain value.
107 | P a g e
7.5 Experimental Results
Fiber sweeps of varying base fluid, density, and fiber concentrations were tested in the flow loop to
evaluate their hole cleaning performance (Section 6). In addition, the data from the XG-based drilling
fluid (WBM) was used to evaluate the mechanistic CTV model shown in Section 7.4. The wellbore
cleaning characteristics observed with the WBM fiber sweeps was subsidiary to the evaluation of the
model.
7.5.1 Comparison of Model Predictions with Test Measurements
The mechanistic model developed in Section 4 was formulated to predict the equilibrium bed height in the
annulus for a given flow rate. The model is valid for annuli without inner pipe rotation. Therefore, to
evaluate the performance of the model, predictions were compared with experimental measurements
obtained without inner pipe rotation. Fig. 7.4 presents dimensionless bed height (H/D) as a function of
flow rate for base fluid and fiber-containing fluid (fiber sweep) in horizontal annulus orientation. For the
base fluid (Fig. 7.4a), the model showed good prediction at low flow rate (up to 50 gpm); however, it
over-predicted the bed height at higher flow rates. Careful examination of results from the model indicate
that the discrepancies between the model predictions and experimental measurements at high flow rates
(more than 50 gpm) could have been due to poor local velocity predictions when the flow protruding bed
particle, which was considered in the mechanistic model analysis, was out of the viscous layer.
(a)
(b)
Fig. 7.4 Bed height vs. flow rate for 2 mm cuttings in horizontal configuration
a) Base fluid, and b) Fiber sweep
The mechanistic model was formulated to account for the presence of fiber in the bed height prediction.
The model predictions for the horizontal test section were compared (Fig. 7.4b) with measurements
obtained from the fiber sweeps. At low flow rates (i.e., less than 60 gpm), predictions showed satisfactory
0.0
0.2
0.4
0.6
0.8
1.0
10 20 30 40 50 60 70 80
Dim
en
sio
nle
ss b
ed
hei
gh
t (
h/D
)
Flow rate (gpm)
Measured (90 deg)
Predicted (90 deg)
0.00
0.20
0.40
0.60
0.80
1.00
10 20 30 40 50 60 70 80
Dim
en
sio
nle
ss b
ed h
eig
ht
(m)
Flow rate (gpm)
Measured (90 deg)
Predicted (90 deg)
108 | P a g e
agreement with experimental measurements. Similar to the base fluid experiments, discrepancies between
predictions and measurements were high at higher flow rates.
Flow loop experiments were also carried out in the inclined annular orientation (i.e., 70º from vertical).
Fig. 7.5 compares the model predictions with experimental measurements in terms of dimensionless bed
height for the base fluid and fiber sweeps. As shown in the figures, the model predictions and
measurements were in good agreement at low flow rate. As previously noted, as the flow rate increased,
the discrepancies between the model predictions and experimental measurements also increased.
(a)
(b)
Fig. 7.5 Bed height vs. flow rate for 2 mm cuttings in inclined (70°) configuration
a) Base fluid, and b) Fiber sweep
7.5.2 Comparison of Model Predictions with Published Data and Existing Model
In order to ensure the accuracy of the model, predictions were compared with published measurements
(Duan, 2005) obtained from large-scale flow experiments conducted to study cuttings transport velocity in
horizontal and highly deviated wells. Two different fluids (water and PAC) and solids particles with
various sizes (0.45 mm; 1.4 mm) were used to perform the experiments. Fig. 7.6 compares experimental
measurements with model predictions for fine cuttings (0.45-mm average diameter) in horizontal and
inclined annuli. A similar plot is presented in Fig. 7.7 for coarse cuttings (1.4-mm average diameter) in
horizontal and inclined annuli. As depicted in the plots, as flow rate increased, the bed cross-sectional
area (bed area) decreased, resulting in an increase in flow area. For coarse cuttings (i.e., 1.4 mm particle),
the new model predictions showed good agreement with the experimental measurements. Discrepancies
increased slightly as the flow rate increased, reaching its maximum value (20 percent difference) at 400
gpm in an inclined annulus. For fine cuttings, the trend was similar and the maximum discrepancy (which
0.0
0.2
0.4
0.6
0.8
1.0
10 20 30 40 50 60
Dim
en
sio
nle
ss b
ed
heig
ht
(h
/D)
Flow rate (gpm)
Measured (70 deg)
Predicted (70 deg)
0.0
0.2
0.4
0.6
0.8
1.0
10 20 30 40 50 60
Dim
en
sio
nle
ss b
ed h
eig
ht
(h
/D)
Flow rate (gpm)
Measured (70 deg)
Predicted (70 deg)
109 | P a g e
was roughly 20 percent) observed was at higher flow rates in inclined configuration. Despite some
noticeable discrepancies at high flow rate, in general the performance of the new model was better than
that of the existing model. The existing model showed discrepancy level of up to 90 percent.
(a)
(b)
Fig. 7.6 Bed area vs. flow rate for 0.45 mm cuttings with PAC based fluid
a) Horizontal (90°), and b) Inclined (70°) orientation
(a)
(b)
Fig. 7.7 Bed area vs. flow rate for 1.40 mm cuttings with PAC based fluid
a) Horizontal (90°), and b) Inclined (70°) orientation
0.00
0.20
0.40
0.60
0.80
1.00
100 200 300 400 500
Ab
ed/A
an
nu
Flow rate (gpm)
Ozbayoglu Model
Mechanistic Model
Measured Data (Duan,2005)
0.00
0.20
0.40
0.60
0.80
1.00
100 200 300 400 500
Ab
ed/A
an
nu
Flow rate (gpm)
Ozbayoglu Model
Mechanistic Model
Measured Data (Duan,2005)
0.00
0.20
0.40
0.60
0.80
1.00
100 200 300 400 500
Ab
ed/A
an
nu
Flow rate (gpm)
Ozbayoglu Model
Mechanistic Model
Measured Data (Duan,2005)
0.00
0.20
0.40
0.60
0.80
1.00
100 200 300 400 500
Ab
ed/A
an
nu
Flow rate (gpm)
Ozbayoglu Model
Mechanistic Model
Measured Data (Duan,2005)
110 | P a g e
7.6 Conclusions
Hole-cleaning performance of fiber-containing sweep fluid was investigated by varying inclination angle,
fiber concentrations, pipe rotation, and flow rate. Experimental measurements showed that adding fiber to
the fluid had a significant effect on the hole cleaning efficiency when applied in conjunction with inner
pipe rotation. Based on the outcomes of this study, the following conclusions are drawn:
• Fiber sweep provides better hole cleaning than the base fluid in horizontal and highly inclined
configurations.
• In the presence of the pipe rotation, adding fiber substantially improves sweep fluid
efficiency. Increasing fiber concentration with pipe rotation tends to improve considerably
the cuttings transport.
• Pipe rotation has a substantial effect on the bed erosion and fiber sweep applications.
• Based on pipe viscometer and rotational viscometer measurements, the quantity of fiber
added to the sweep fluid has a minor effect on rheological and hydraulic characteristics of the
fluid.
• Mechanistic modeling provides better prediction than the existing model.
• Cuttings transport model predictions agree with the experimental data at low flow for both
base fluid and fiber-containing fluid.
Nomenclature
AP = projection area of a particle
Af = flow area above the cuttings
A = constant
B = constant
CDv = viscous drag coefficient
CL = lift coefficient
CDf = Fiber drag coefficient
Cϕ = correction of the angle of repose
C = fiber concentration
dp = diameter of a particle
Dh = hydraulic diameter of a layer
Deff = effective diameter
dVr/dy = velocity gradient
ReP = particle Reynolds number
Re = Reynolds number
ReG = gradient Reynolds number
So = wetted perimeter of the outer wellbore
Si = wetted perimeter of inner drill pipe wall
Sb = wetted perimeter of the cuttings bed
t = Time
U= mean flow velocity in the channel
U max = maximum fluid velocity in the channel
Uτ = friction velocity
u+ = dimensionless velocity
Vr = local velocity at the center of a bed particle
V = Instantaneous settling velocity of a particle
111 | P a g e
dp+ = particle diameter dimensionless
Dr = correction factor of the drag coefficient
Fb = buoyancy force
FD = drag force
FDf = fiber drag force
fbed = friction factor of the bed
FL = lift force
f = friction factor
FDT = total drag force
FDv = viscous drag force
Fg = gravitational force
Fp = plastic force
g = gravitational acceleration
K = consistency index
k' = equivalent consistency index
m = mass of a solids particle
n' = equivalent fluid behavior index
n = fluid behavior index
p = pressure
Vs = Terminal settling velocity of a particle
y = vertical distance from the mean bed level
y+ = dimensionless distance
Greek Letters
Гp = rotating torque at point p
ε = pipe roughness
∏ = angle of repose
α = angle of inclination from vertical
α = exponent power of the fiber concentration �� = Shear rate
δ+ = dimensionless of thickness laminar sub-layer
µ = fluid viscosity
ρf = Fluid density
ρp = density of a particle Ë= kinematic viscosity
τy = yield stress
τbed = average bed shear stress
τw = wall shear stress
τdis = shear stress distribution around a bed particle
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